The sum of the digits of a two-digit number is 9. if the digits are reversed, the new number is 27 less than the original. find the original number.

I did another one just like this about an hour ago.  I did it the elegant, tedious way,
and it took about 2 feet of screen.  Then I realized there was a totally bourgeois but
easy way to do it.  For 5 points, I'll give you the method for the masses:

List all the possible pairs of digits that add up to 9, along with their flips:

18 . . . . . 81
27 . . . . . 72
36 . . . . . 63
45 . . . . . 54

Do you see any pair that are different by 27 ?
How about 36 and 63 ?

So the original number is 63, and when you flip it, it becomes 36, which is 27 less.