The correct option is E Dickinson, which were written over a period beginning a few years before Susan's marriage to Emily's brother and ending shortly before Emily's death in 1886, outnumber
In option A, though the noun 'letters' agrees with the verb 'were written', the use of the participle 'outnumbering' is incorrect. "Outnumbering" works as a modifier here but it does not seem to modify the preceding 1886. So A is out. B has two verbs 'were written' and 'outnumber' without anything joining them. Thus, B is incorrect. C has two participles ('written' and 'outnumbering') with no verbs at all. Though the inside of the clause( '...which were written...') in D is correct, the use of the participle 'outnumbering' outside of the clause renders the sentence incorrect- as there's no verb in the independent clause of the sentence, it remains incomplete. E avoids all these errors and becomes the correct choice.