When you add a sum to a (positive) difference, you get twice the larger number because
(a + b) + (a - b) = a + b + a - b = a + a
For example, if the sum was 13 and the difference was 5, then the sum + the difference is 18. That's twice the larger number, so the larger number is 9. But that means 9 plus something equals 13, and that other number must be 13 - 9 = 4.
Now try it with your numbers.
Stephen La Rocque>
Here is another solution to Sue's problem where the sum is 13 and the difference is 5.
If the sum of two numbers is 13 and the difference is zero then each of the two numbers would be 13/2 = 6 1/2. But the difference you want is 5 so one of the numbers is 2 1/2 less than 6 1/2 and the other is 2 1/2 greater than 6 1/2. Thus the two numbers are
6 1/2 - 2 1/2 = 4 and 6 1/2 + 2 1/2 = 9.