Sum 15 difference of 5

The numbers would be 10 and 5
The explanation for this is because

The sum of x and y would be 15 or in other words x+y=15

Though the difference of x and y or x-y is 5.

x-y=5
x=5+y

You would then replace x from the first equation to the 2nd equation

x+y=15
5+y+y=15
5+2y=15
2y=10
y=5

So if we know that y is 5, we also know we should substitute y for 5.
x+y=15
x+5=15
x=10

Now we know that x is 10.
So the sum if two numbers are 15 and their difference is 5. If we were to ask ourselves ‘what are the two numbers?’ the answer would be
Sum: 10+5=15
Difference: 10-5=5