Take Any Number ...

Not if you can't remember your original number!

Just as math gives you the tools to make things work, ultimately some mathematician will give you a tool to break things by removing assumptions. Try it out with modular arithmetic with some careful choice... like the value 2 mod 4:
2*(2 mod 4) = 0 mod 4
(0 mod 4) + 10 = 2 mod 4
(2 mod 4) / 2 = 1 mod 4 (definition of division in modular arithmetic is tricky)
(1 mod 4) - 2 = 3 mod 4

Although modular division is kind of tricky, and there are two possible values x, such that 2x = 2 mod 4: the 1 mod 4 used above, and 3 mod 4, for which 3 mod 4 - 2 = 1 mod 4 = 5. So it can still work, but for only one of the possible outcomes of the division.