It looks like the answer is
spacetime (Thanks Deusovi!)
Much of the riddle clues
Whitespace, an esoteric programming language (Again, thanks Deusovi!)
My first is nothing at all
or maybe everything combined.
White can be thought of as colourless or all colours combined
Adding or subtracting,
just depends how it's defined.
White is colourless in a subtractive colour model, and all colours together in an additive colour model.
My second is everything combined
Space is sometimes used to refer to the universe, which is certainly everything combined (thanks noedne!)
or maybe nothing at all.
Space is a vacuum, which is nothing
It took us years to get there,
though there is no wall.
It took a long time to develop space technology
Together I'm nothing at all,
but with both halves combined
Whitespace is "nothing", as it just spaces words and paragraphs
I am right at the source,
here for you to find.
The riddle is actually source code for a Whitespace program that outputs the word "spacetime"!