"Having written the letter, he sent it."
Translation:Skribinte la leteron, li sendis ĝin.
Estis skribinta in your example doesn't have a subject. In English, we use a participle adverbially, "Having written the letter...", but in Esperanto, you have to make it explicit that this phrase is an adverbial description of the main idea. That's why it has to be skribinte.