Let represent the larger of the two digits. Let represent the smaller. We know that they have to be different, and therefore there exists a smaller and a larger because the difference is non-zero.
The difference of the digits is 5:
The difference of the squares is 45:
Add to both sides of the first equation:
Substitute for in the second equation:
Expand the binomial and simplify:
Now you know that one of the digits of your two digit number is 2.
Go back to the first equation:
Now you know that your two digit number is either 72 or 27. Only one of these is odd.
John
My calculator said it, I believe it, that settles it
