To solve this problem we have to make system of equations.
\(\left \{ {{a+b=52} \atop {a-b=20}} \right.\)
From the first equation lets find value of a in times of b
a=52-b
Now we can substitute it into second equation
52-b-b=20
52-2b=20 /-52 both sides
-2b=20-52
-2b=-32 :(-2) divide both sides by -2
b=16
Now we can back substitute to the first equation
a=52-b
a=52-16
a=36
So the result is
\(\left \{ {{a=36} \atop {b=16}} \right.\)