The sum of two numbers is 30 in the difference is 12 find the two numbers

Let's call the numbers x and y:

their sum is:

x+y=30

and their difference is x-y=12.

from the first equation: x=30-y

and we insert this into the second equation:
30-y-y=12.

we calculate:

30-2y=12

30-12=2y
18=2y
9=y

so the first number is 9 and the second is 30-9=21.