Me, Myself
Pronoun and の adjective
わがはい
吾輩が貴殿に久しく手紙を書いていなかったことをどうかお許しください。
Please forgive me for not writing to you in such a long time.
I, my comrade (which is me), is I, it's myself, it's me. This is a weird way to say "I" and has a hint of arrogance to it.
The reading comes from the readings you learned with the kanji readings.