Here is a typical English vowel chart: As you can see, /æ/ and /ɛ/ are quite close to each other, and so have quite a similar sound.
The difference is in the degree of openness: /æ/ is “near-open” and /ɛ/ is “open-mid”.
If you want to make a clear distinction between the two, you need to practice, practice, practice.
When I was learning phonetics, I found the best practice was to try to make long continuous vowels that go along the axes, like /iiiiiiiieeeeeeeeɛɛɛɛɛɛɛɛææææææææaaaaaaaa/.
Once I was able to master making the entire continuum, it became easier to find individual points along the continuum.
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As I don't know Turkish, so I'm afraid I can't give you examples of pronunciation in your native language, but this may still help: salary: SAH - lah - ree celery: CELL - lair - ree
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Celery e as in evetSalary as the e in lütfen
You could pronounce salary just as if it were a Turkish word as well.
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The /æ/ sound (which in American English is the sound present in words like cat , gap , fan , man ) is pronounced by dropping your jaw down as if you were going to say [ä]; then from that position try saying /ɛ/.
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@Mehper
C. Palavuzlar
The easiest thing you can do in keeping the difference between [ɛ] and [æ]is to pronounce every [æ]
like [a].
I know most people don't even realize a simple fact that for most British people [æ] is quite a foreign sound.
In the Midlands, Northern Britain, Scotland, Wales, Ulster and Ireland [a] is the most usual, typical realization of [æ].
The same is true for both Canadian and Caribbean dialects &/or accents.
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The most dictionaries I consulted show that the first e in celery is IPA e (seləri).
Read what the important phonetician Daniel Jones said about æ The correct sound of æ can generally be obtained by remembering that æ must have a sound intermediate in quality between ɛ and a .
In practising the sound, the mouth should be kept very wide open.
The sound may be obtained by imitating the baaing of a sheep which is very like ˈbæː .
Those who are unable to obtain the exact quality by practising such exercises should note that it is better to err on the side of
a rather than on the side of ɛ (my emphasis) .
a is actually used for æ in some parts of the North of England.
(Note 401 in this book ).
I also noticed the emphasized part from my own experience with words such as happy and laptop .
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You might subscribe to a podcast located at speakmoreclearly.com which offers phonological analysis and pronunciation practice of English accents (British, American and Australian).
Repeated practice on this sentence will do wonders: '
Yet another white man doomed to rot under the tropic sun!'
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For a non-native English speaker like me, it's always been hard to sound æ and ɛ differently. For example, "salary" and "celery" are two words that I tend to pronounce identically.  Is it OK to go on like this or should I practice to get it right?
How can I practice differentiating between the "æ" and "ɛ" sounds in English phonology?
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english.stackexchange.com/users/127/Mehper C. Palavuzlar
The answer to this will be subjective, but the main way to practice differentiating between these two vowel sounds will probably involve a lot of repetition and tryng to make long, continuous vowels that go along the axes. With these particular vowel sounds, you will want to keep your mouth very wide open.  The most important thing is to practice a lot and form the right shape with the mouth and jaw, taking words that give good examples of these sounds.
The answer to this will be subjective, but the main way to practice differentiating between these two vowel sounds will probably involve a lot of repetition and tryng to make long, continuous vowels that go along the axes. With these particular vowel sounds, you will want to keep your mouth very wide open.  The difference is in the degree of openness: /æ/ is “near-open” and /ɛ/ is “open-mid”.  If you want to make a clear distinction between the two, you need to practise. For most British people [æ] is quite a foreign sound. In the Midlands, Northern Britain, Scotland, Wales, Ulster and Ireland [a] is the most usual, typical realization of [æ].
One practice technique is to try to make long continuous vowels that go along the axes. For example: iiiiiiiieeeeeeeeɛɛɛɛɛɛɛɛææææææææaaaaaaaa. You could also pronounce salary as though it was a Turkish word. The speakmoreclearly.com podcast also offers phonological analysis and pronunciation practice of English accents. There are many different pronunciation practice techniques available. For example, you could try identifying similar sounds in Turkish. You could also consider practising a long sound which passes through all the vowels. There are also online resources such as speakmoreclearly.com which could help you with your pronunciation.
Try making all the sounds on the continuum and then pick out the individual one. Drop your jaw down and then say it;. Keep the mouth wide open when practising.
The difference is in the degree of openness: /æ/ is “near-open” and /ɛ/ is “open-mid”.  If you want to make a clear distinction between the two, you need to practise. For most British people [æ] is quite a foreign sound. In the Midlands, Northern Britain, Scotland, Wales, Ulster and Ireland [a] is the most usual, typical realization of [æ]. You might subscribe to a podcast located at speakmoreclearly.com which offers phonological analysis and pronunciation practice of English accents (British, American and Australian).
One way of practising particular vowels would be to make one long continuous sound that passes through all of them. You could try to identify the Turkish sounds that are similar. There are online tools, such as speakmoreclearly.com which can help your pronunciation.