AT THE END / IN THE END

At the end(of something) = at the time when something ends.
at the end of the month. at the end of the film.
at the end of January. at the end of the course.
at the end of the match. at the end of the concert.

I´m going away AT THE END of January.
AT THE END of the concert, there was great applause.
All the players shook hands AT THE END of the match.

You cannot say 'in the end of something'.So you cannot say 'in the end of January' or 'in the end of the concert'.
The opposite of AT THE END is AT THE BEGINNING
At the beginning of January. At the end of the concert

In the end = finally

We use IN THE END when we say what the final result of a situation was
We had a lot of problems with our car.IN THE END we sold it and bought another one. (=finally we sold it)
He got more and more angry.IN THE END he just walked out of the room.
Jim couldn´t decide where to go for his holidays.He didn´t go anywhere IN THE END.

The opposite of IN THE END is usually AT first.
AT FIRST we didn´t like each other very much, but IN THE END we became good friends.