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)

38+105= 143, 39+104=143, and you will find then adding the numbers on opposite sides, moving inwards yields the answer 138 every time. because of this, you’re going to multiply 138 times the number of pairs, which is 34. therefore, 34*138= 4692(i’m sorry if it’s the wrong numbers, but it’s the right concept)