The sum of the digits of a two-digit counting number was 13. when the digits were reversed, the new number was 9 less than the original number. what was the original number?

So the number is xy ( this doesn't mean x times y)
x+y=13
yx=xy-9
the digits cannot be the same
they must add up to 13 so they cannot be positive so the number pairs are single digits so
9+4
8+5
7+6
the possible numbers pairs are
94 and 49
85 and 58
76 and 67
we find the differences
94-49= greater than 9
85-58= greater than 9
76-67=9

the original number is 76

With a continuous thought process.