The sum of the digits of a two-digit number is 8. when the digits are reversed, the number increases by 36. find the original number.

You can represent a two digit number with vars x, y as x*10+y

I:x+y=8
II:reversed=original+36:
y*10+x=36+10*x+y=
=y*9=36+9*x
=y=4+x

insert y into formula I:
=x+y=8
x+(4+x)=8
2x+4=8
2x=4
x=2

So the original number is x*10+y=26

x=2 y=6
I: 2+6=8
II: 6*10+2=2*10+6+36=
=60+2=26+36=62