The way it is written is misleading at best for anyone trying to solve it as a math problem.
Really, all it is is a table of values. x, y, a, b; where a = x-y and b = x+y
If x and y are known, you can solve a and b.
If a and b are known, you can solve x and y. Something something solve for x then y (or y then x respectively);
x = a+y
b = (a+y)+y
23= 1+2y
y=11
1=x-11
x=12
<x=12, y=11, a=1, b=23>
But, being that it was set up as pattern recognition, and not actual mathematics...