if x and y are the numbers, then you have the following system of equations:
x + y = 82
x - y = 34
in order to solve the previous system, proceed as follow:
add the equations:
x + y = 82
x - y = 34
2x = 116
divide by 2 the previous equation to obtain x:
x = 116/2
x = 58
next, replace the previous value of x into any of the equation os the system, and solve for y:
x + y = 82
58 + y = 82
subtract 58 both sides:
y = 82 - 58
y = 24
Hence, the solution of the system of equations is
x = 58
y = 24