One possible pair of numbers with a sum of 13 and a difference of 5 is 9 and 4. To see why this works, consider that the two numbers can be represented as x and y, where x is the larger number and y is the smaller number. The sum of x and y is 13, so we have x + y = 13. The difference between x and y is 5, so we have x - y = 5.
By substituting the second equation into the first, we can find x:
x + y = 13
x = (x + y) - y = 13 - y
x - y = 5
x = (x - y) + y = 5 + y
Setting these two expressions equal to each other, we have:
13 - y = 5 + y
18 = 6 + 2y
12 = 2y
y = 6
Therefore, the two numbers with a sum of 13 and a difference of 5 are x = 5 + 6 = 11 and y = 6.