x = first number
y = second number
The sum of two numbers is 17, so
x+y = 17
Their difference is 7, so
x-y = 7
We have this sytem of equations
x+y = 17
x-y = 7
Add up the equations to get
x+y = 17
x-y = 7
--------
2x+0y = 24
So 2x = 24 which means x = 12 after you divide both sides by 2 to isolate x.
Use x = 12 to find the other number.
x+y = 17
12+y = 17
12+y-12 = 17-12
y = 5
So the second number is y = 5