Question: Let's say user A follows user B, and B follows A. I want to know the exact date A started following B and viceversa.
Is this information stored on twitter? Can I retrieve it using the API?

To clear out: The point of this question is finding a way to know who followed who first.
(I'm assuming both A and B deleted the notification e-mails)

Answer: 
This is a very old question, but perhaps some might be interested to know that while you cannot get the date at which someone started following, you can at least infer an "earliest possible following date" from the fact that the list of followers is ordered according to date, and the fact that follower objects come with a `created_at` timestamp. 

Here's a Python function for calculating an "earliest possible following date": <https://github.com/BernhardClemm/twitter-follow-dates>
It is possible to do this, but impractical. When you call the followers API you can page the results. Each returned object contains `next_cursor` and `prev_cursor` items. These refer to the first and last records in the next and previous pages. These values are time based and can be used to calculate the time that the respective users followed you.

It follows that, if you set the page size to `1`, you can walk through the list of follower IDs one at a time and the `next_cursor` value will allow you to derive the follow time for the next record.

This is reasonably simple to implement, however, in practice, you'll very quickly hit Twitter's API rate limit.