hey I'm in the same class as you, and stuck on this as well. This is what I have so far.
I'm going off the direct proof structure of the existential (chapter 3.7)
This is my general structure:
Let $a = 40$ and $b = 24$.
Then $a \in \Bbb Z_+$ and $b \in \Bbb Z_+$.
Then $$a+b=40+24=64=8^2 \tag a\label a$$
and
$$a-b=40-24=16=4^2 \tag b\label b,$$
so $$a \in \Bbb Z_+,\quad b \in \Bbb Z_+,\quad a+b=x^2,\quad a-b=y^2 \tag c\label c$$
I'm not really sure how to format it properly. Also I'm not sure if line \eqref{a} and line \eqref{b} can/are supposed to be combined like what I did on line \eqref{c}. I'm not even sure if line \eqref{c} is correct format wise...