Dear Amna 107,
I didn�t have the book in my hand to answer to your question inmediately
but here you have some information taken from
Practical English Usage by Michael Swam that may be useful
in the end suggests that something happens after a lot of changes, problems or uncertainty.
eg, We made eight different plans for our holiday, but in the end we went to Brighton again.
at the end simply refers to position at the end of somenthing. There is no sense of waiting or delay.
eg, I wish I was paid at the beginning of the week and not at the end.