Yeah I mean... first you have to pick a 2 digit number. We'll have XY as ours (one letter for each digit).
You are supposed to add X and Y together then subtract them from XY. The addition is just a distraction though.
XY - (X + Y) = XY - X + -Y.
Just subtract Y first. Now you have X0. So before you subtract the ones position you are guaranteed to have X0. Everytime. Basically although you have "free choice" you really are limited to 10, 20, 30, 40, 50, 60, 70, 80, and 90. And you are then forced to subtract X which is the tens digit. Therefore you'll either get 9, 18, 27, 36, 45, 54, 63, 72, 81. Which are all divisible by 9.
Any time you are given free choice of a number and told to manipulate it... you're manipulating it towards a known.