The difference between a two-digit number and that number reversed is 18. what could that number be? list all possibilities.

A two digit number can be written like AB or 10*A + B ( for example the number 36 can be written like 3*10 + 6 = 36)
You can write this problem as

10*A + B - (10*B + A) = 18
10*A + B - 10*B - A = 18
9*A - 9*B = 18
9(A - B) = 18
A - B = 2

A and B are digits, that means that both are either 0,1,2,3,4,5,6,7,8 or 9 (except that A cannot be 0 bcs the first digit in a two digit number cannot be 0)

So the combinations are

9 - 7 = 2
8 - 6 = 2
7 - 5 = 2
6 - 4 = 2
5 - 3 = 2
4 - 2 = 2
3 - 1 = 2
2 - 0 = 2

And we have the numbers:
97 ( B is 79)
86 ( B is 68)
75 ( B is 57)
64 ( B is 46)
53 ( B is 35)
42 ( B is 24)
31 ( B is 13)
20 ( B is 2)