这个长句可以这样分析：
He wrote me a letter,telling me his trouble
he asked me for advice
worte和asked用过去式是因为这两个句子中间用and连接,用and连接的两个句子时态要一样.
其中He wrote me a letter,telling me his trouble是一个长句,telling me his trouble是一个分句,修饰letter,指这封letter写了什么,一个句子不能有两个动词,所以tell要不用told,要不用telling,因为“他”写了这封信并告诉我trouble,是主动的,所以用telling.