I am thinking of three numbers. When I add them up, I get 15. When I subtract the third number from the sum of the first two, I get 10. When I subtract the second number from the sum of the first and third, I get 8.

Which numbers am I thinking of?

(E. Semerádová)
Let's consider the sum of the first two numbers. If Eva (the author of the problem) adds the third number to this sum, she gets 15; if she subtracts the same number, she gets 10. The difference $15 - 10 = 5$ thus corresponds to twice the third number. Therefore, the third number is $5 : 2 = 2.5$.

Let's consider the sum of the first and third numbers. If Eva adds the second number to this sum, she gets 15; if she subtracts the same number, she gets 8. The difference $15 - 8 = 7$ thus corresponds to twice the second number. Therefore, the second number is $7 : 2 = 3.5$.

The sum of all three numbers is 15. Therefore, the first number is $15 - 2.5 - 3.5 = 9$.

Eva is thinking of the numbers 9, 3.5, and 2.5.

Note. The problem can be expressed using a system of equations

$$
a + b + c = 15, \quad a + b - c = 10, \quad a - b + c = 8
$$

where $a, b$, and $c$ represent the first, second, and third numbers, respectively. The previous reasoning can be written as follows:

$$
\begin{gathered}
2 c = (a + b + c) - (a + b - c) = 15 - 10 = 5, \quad \text{thus} \quad c = 2.5, \\
2 b = (a + b + c) - (a - b + c) = 15 - 8 = 7, \quad \text{thus} \quad b = 3.5, \\
a = (a + b + c) - b - c = 15 - 2.5 - 3.5 = 9.
\end{gathered}
$$