How can I find lines in one file but not the other using bash scripting?

Imagine file 1:

#include "first.h"
#include "second.h"
#include "third.h"

// more code here
...

Imagine file 2:

#include "fifth.h"
#include "second.h"
#include "eigth.h"

// more code here
...

I want to get the headers that are included in file 2, but not in file 1, only those lines. So, when ran, a diff of file 1 and file 2 will produce:

#include "fifth.h"
#include "eigth.h"

I know how to do it in Perl/Python/Ruby, but I'd like to accomplish this without using a different programming language.