Define E to be the set of even integers; E = {$x$ $\in$ $\mathbb{Z}$ : $x$ = 2$k$, where $k$ $\in$ $\mathbb{Z}$}. 

Define F to be the set of integers that can be expressed as the sum of two odd numbers.

Prove E = F.

My attempt: The only way I can figure out the solution is by providing numbers and examples. It's easy to see that two odd numbers will always equal an even integer. I just don't know how to write the proof for it.