You have a two digit number.  When the digits are added, the sum is 7.  When you reverse the digits and subtract from the original number, the difference is 9. What is the 2 digit number?

Let's examine what numbers add to 7.

1 and 6
2 and 5
3 and 4

You know the original number must be larger than the second number, so the original number must be 61, 52 or 43.

When reversing the numbers you get 16, 25 and 34.

Now let's subtract

61 - 16 = 45
52 - 25 = 27
43 - 34 = 9

The original number is 43.

The easy way to know it must be 43 is to get a 9 when subtracting, the second number must be 1 greater in the one's place than the original number.  4 is 1 greater than 3.