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I would like to express my deepest apology for I left without saying good-bye two days ago. And I am writing the letter to you because of(加定冠词the)sincere friendship between us. I am sorry to cause you(加to be) sorrowful. I wish to explain the reason why I have to do so.(看完这句话会以为你第二段将要解释为什么没有说再见就走了) On the one hand, I am very grateful to you and your family for the hospitality when I study in your local school. On the other hand, I believe our real friendship is one of the most precious emotions in my life, and a little worriment is in my heart once I have to say goodbye. Please allow me to say sorry again. And we will always be friends. | 
