When the digits are reversed, the number increases by 36. find the original number

We can write the original number like this:

x*10+y,

where x and y are the digits, so the number would look like this: xy

and we know that if we inverse, i. e. y*10+x, we will get the original number plus 36:

y*10+x=x*10+y+36

let's move all the ys and xs to the left:

10y-y+x-10x=36

9y-9x=36

let's divide by 9:

y-x=4

so the difference between the digit is 4, and x is smaller

this could mean that it could be any of these numbers:

15

26

37

48

59

next possibility: x=6 woould make y=10, so it would no longer hold.