Hello London,
If x and y are those numbers:
the sum of 2 numbers is 30 ---> x + y = 30
and their difference is 10 -------> x - y = 10
You can add both equations and you get: x + x + y - y = 40 ----> 2x = 40 ----> x = 20, so one of the two numbers is 20.
Replace x by 20 in either equation. You now have 20 + y = 30, you can solve for y and that will be the other number.