Dear xxx:
Hi.I am writing to you to apologize for my words and behaviour.You know that the book you lost was one of my favourite books.I really loved that book.And that was why I was so angry and sad when I heard that you lost it.We haven't talked to each other since our quarreling.But I still keep our friendship in my mind.I hope that you can forgive me for my mis-doing.I am sorry for that.But I really wish that you will be careful with your things in the future.You know carelessness can do great harm to you in your study and work as well.
Let's be good friends again.I really miss the good relation with you.
Best Wishes!
Yours,xxx