I'm having a problem wrapping my head around something...

I need to have a piece of code that will compare two text files (technically .ini files, but same idea) and then update FileA with any data it's missing from FileB.

Example:
FileA has 3 lines
Code:
Bob
Jim
George
FileB has 5 lines
Code:
David
Susan
Jack
Jim
Bob
I need to update FileA with the names it is missing without removing any that it already has (or create a new file with combined information but no duplicates).

For some reason, I cannot figure this out without making some really ugly code. (Which hasn't worked right either)

Any help is greatly appreciated!