Question: I've been having this doubt for a quite a while and haven't been able to find a satisfying answer. Is the 'E#' note technically an F? If so, why does it not exist on the chromatic scale like other sharps? I mean, what exactly is the E#? Is it a note on its own or is it just another way of saying F?

And what do people mean when they say that the D# Major scale is theoretical major scale and why it does not exist in the circle of fifths diagram?

I came across the last paragraph on a website.

Answer: 
1. E-sharp is called the enharmonic equivalent of F-natural. The sharp raises the base note one half step. In the same way B-sharp is the enharmonic respelling of C-natural. Furthermore, C-flat is the enharmonic of B-natural, and F-flat enharmonic of E-natural. Notes may also be double-sharped and double-flatted, which raises the base note by two half steps.
2. The key of D-sharp could be considered a theoretical scale because it doesn’t appear on the basic circle of fifths is simply because it is a scale that contains these enharmonics, and traditionally composers write this as E-flat to avoid the enharmonic spelling of the second scale degree, F-natural, which is enharmonic with E-sharp, the second degree of D-sharp major, and no one likes reading parts with double-sharps in the key signature (shudder). The seventh degree of the D-sharp major scale is C-double-sharp. D-sharp major chords definitely exist in music and we play enharmonic spellings all the time.
E# is not technically F, only in equal tempered tuning. That's the first cause of concern.

The degrees of any scale follow a sequence and that sequence is never broken. The note names follow the "musical alphabet" {A, B, C, D, E, F, G} then repeat. Accidentals are needed to preserve the whole step - half step sequence {1, 1, 1/2, 1, 1, 1, 1/2} which is two tetra chords separated by a whole step. The numbered degrees are simply {1, 2, 3, 4, 5, 6, 7}. So for example, in the Key of E the degree letter names are {E, F, G, A, B, C, D} repeat. To preserve the steps we raise or lower notes as needed, for this example we get {E, F#, G#, A, B, C#, D#}. The second degree of E is always an F of some sort (period). Now in your example the key is D#. The correct way to name notes is to take D and just make everything #, Key of D = {D, E, F#, G, A, B, C#}. The key of D# would be {D#, E#, F##, G#, A#, B#, C##}. If the E# bothers you, why not ask about the futility of F## and C##? Using enharmonicity of the equal tempered tuning one would usually notate this key as Eb, which takes a lot less effort to notate correctly.