Question 953173
let
x = tens digit 
y = ones digit

sum of digits of two-digits number is 7
x+y=7

reversing its digits increases the number by 9
10y+x=(10x+y)+9

now you got a system of equation, you can solve for two variables.

the answer x=3 y=4

you can find two number and test it out, it will be more easy to understand. (ex. x= 3 y=4)

i would lvoe to hear alternative ways to solve it, gmail me if you have one
adamchen894@gmail.com