I've seen many examples of this type of world problem, but the numbers are usually much smaller. The most important thing to understand is that the two numbers are unknown, but these equations give clues as to what they are. since they are unknown, and there are two of them , lets go with x and y.
Sum of two numbers... x+y= 533
Difference of two numbers.... x-y=269
The next important thing to grasp is the fact that algebra requires a lot of manipulation so you can find order in a what seems like a lot of chaos.
you may or may not have learned that when two equations both equal the same thing, it means you can equal them to each other. (x=5+y, x=11-y can be changed to 5+y=11-y) So in this problem, first you subtract y from x+y=533
x+y(-y)=533(-y) -> x=533-y
then you add y from x-y=269
x-y(+y)=269(+y) -> x=269+y
then you equal them to each other and it becomes 533-y=269+y, now you simplify
533-y(+y)=269+y(+y)
533=269+2y
533(-269)=269(-269)+2y
264=2y
Divide each side by 2 and you will get 132.
y=132, now plug y into an original equation like x-y=269
x-132=269, add 132 to both sides and you'll get 401.
x= 401, y=132.
Check your work, 401+132=533 and 401-132=269! Nice!
