Question 227231
Well lets call the two numbers x and y.  We know that x+y = 34 and x-y 18.  So now we have 2 equations and 2 unknowns.

x+y=34
x-y=18

Now we add both equations and find that 2x = 52 so x = 26.  Now we plug that value into the first equation and find that y = 8.