Suppose two numbers are x and y. By the statement of the problem we will get the following
x+y=34 eq 1from here x=34-y
put in the second equation
x-y=10 eq 2
34-y-y=10
34-2y=10
2y=34-10
2y=24
y=12
put in eq 1
x+12=34
x=34-12
x=22 so the two numbers are 22 and 12
x+y=34 eq 1from here x=34-y
put in the second equation
x-y=10 eq 2
34-y-y=10
34-2y=10
2y=34-10
2y=24
y=12
put in eq 1
x+12=34
x=34-12
x=22 so the two numbers are 22 and 12