|x-(45-x)| < 10

|x-45+x| < 10

|2x-45| < 10

|x-22.5| < 5

-5 < x-22.5 < 5

Add 22.5 to all three sides:

17.5 < x < 27.5, so x e {18,19,20,21,22,23,24,25,26, 27}

 1. (18, 27)
 2. (19, 26)
 3. (20, 25)
 4. (21, 24)
 5. (22, 23)
 6. (23, 22)
 7. (24, 21)
 8. (25, 20)
 9. (26, 19)
10. (27, 18)

If you meant that the absolute difference must be less than 10 then that is
the correct list and 10 is the answer.

If you meant the difference to be "first-second" then it's just the last 5.
The answer is 5.

So the answer is 5 or 10 depending on whether you mean absolute difference
or first minus second.

Edwin