This is a quotation from Chekhov's story "Тоска"(See https://ru.wikisource.org/wiki/%D0%A2%D0%BE%D1%81%D0%BA%D0%B0_(%D0%A7%D0%B5%D1%85%D0%BE%D0%B2)#cite_note-1). I have googled but couldn't find anything about the meaning of the word "повем".
This is the first line of a spiritual chant called Стих плача Иосифа Прекраснаго, егда продаша братия его во Египет ("A verse of lamentation of Joseph the Most Beautiful when his brethren sold him into Egypt").
It means "to whom shall I tell of my sorrow".
Повем here is a rendition of the Church Slavonic form повѣмь ("I will tell", literally "I will let know").
It's one of a small bunch of so called athematic verbs, whose conjugation endings lacked vowels and attached directly to stems. There were more verbs like that in Proto-Indo-European but only a few of them remained in Proto-Slavic.
There were five such verbs in Church Slavonic: быти "to be", дати "to give", вѣдѣти "to know", ѣсти "to eat", имѣти "to have".
Two of those verbs retained the athematic endings in modern Russian: я ем, я дам, others have lost it: поведаю is the modern Russian way of saying повѣмь.
A couple of athematic forms are fossilized in set phrases like бог весть ("God (only) knows"), власть имущие ("the powers that be", literally "those who have power") etc.