let the numbers are x and y
The sum of the numbers is 12
So, x + y = 12
the difference between the numbers is 4
So, x - y = 4
The system of equation will be:
[tex]\begin{gathered} x+y=12\rightarrow(1) \\ x-y=4\rightarrow(2) \end{gathered}[/tex]Add the equations to cross y then solve for x
[tex]\begin{gathered} (x+y)+(x-y)=12+4 \\ x+y+x-y=12 \\ 2x=16 \\ x=\frac{16}{2}=8 \end{gathered}[/tex]substitute with x into equation 1 to find y
[tex]\begin{gathered} 8+y=12 \\ y=12-8 \\ y=4 \end{gathered}[/tex]so, the answer will be the numbers are 8 and 4