I’ve been working on a document that described a number of buildings with annexes, and I have to admit that I had to look this up, just to check. Well, to be honest, I look up a lot of things to check them, as I’d always rather get it right, oddly enough (one of these days I’ll write a post about a word that I’ve always thought is a word, but doesn’t actually exist …)
So, to annex is a verb, never has an e on the end, and means to add as an extra part or to appropriate territory. I can’t give an example of the latter without getting all political, but you could have a set of tables and a document they refer to, and decide to annex the tables to the document rather than present them separately. That’s an acceptable, discrete verb form, not one that’s been oddly made out of a noun (like “to inbox” – ugh) as far as I know.
An annexe, the noun, is an addition to a document or building. Now, I have to admit that I thought the difference lay here, and that the e was only added for a building. But all of my good old Oxford sources say no, it’s used for both. So, “The table was added as Annexe 1 to our document”; “Coffee will be served in the annexe to the church”.
Or, you can just skip the e there altogether. But you know me: I like to maintain different forms of words to preserve the variety of our language. So I say verb: no e; noun: add that e. Add it as an annexe, if you will!