The sum of two numbers is 30 and their difference is 2. find the two numbers by writing and solving a
system of equations

The numbers are 14 & 16.

The equations you need to solve are:

x + y = 30
x - y = 2  ==>  (redefine in terms of y)  y = x - 2

substitute into first equation

x + x - 2 = 30
2x = 30 + 2
x = 32/2 = 16

16 + y = 30
30 - 16 = y = 14

x = 16
y = 14

And that's how that is done.