Question 44442
Use x and y because we do not know the value of either number.
(x)+(y)=34 because the "sum" means to add.
(x)-(y)=10 because the "difference" means to subtract. 
 .
Solve using either the substitution or addition method for solving systems of linear equations:
.
-(x+y=34) 
+(x-y=10) 
_________
    
.
.
-x-y=-34 
+x-y=+10 
_________
0-2y=-24
.
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Solve for y:
-2y=-24
-y=-24/2
y=12
.
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Plug y=12 back into the original equations and solve for x:

x+y=34 
x+12=34
x+12-12=34-12
x=22
.

x-y=10
x-12=10
x-12+12=10+12
x=22
.
.
Checking that x=22 and y=12:
22+12=34
22-12=10
The values check out.