Set on of the numbers as x. The consecutive integer to it would be x+1 (or x-1, which ever one you like. I'm going to use x+1 though).
The sum would be
x + (x+1)
Set it equal to 59.
x+x+1=59
2x+1=59
2x=58
x=49
One integer is 49. The other integer, x+1, is 50.
Hope this helps!
