All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and messenger.
You mentioned that the Quran and the Sunnah say nothing about the issue in question, but this is not true. Rather, Allaah says (what means): {O you who have believed, protect yourselves and your families from a Fire whose fuel is people and stones, over which are [appointed] angels, harsh and severe; they do not disobey Allaah in what He commands them but do what they are commanded.} [Quran 66:6]
Ibn Abbaas interpreted protecting one's family in this verse as meaning, “teach them and discipline them.”
Besides, Ibn 'Umar narrated that he heard the Prophet saying: “... and the man is a guardian in his home and will be questioned for the people under his guardianship...” [Al-Bukhari and Muslim]
So how can a man be ordered to teach righteousness to his wife, discipline her and protect her from what leads her to Hellfire and be questioned about her on the Day of Judgment in front of Allaah and at the same time be permitted to allow her to have unlawful relationships with men? Allaah says (what means): {Indeed, those who like that immorality should be spread [or publicized] among those who have believed will have a painful punishment in this world and the Hereafter. And Allaah knows and you do not know.}[Quran 24:19]
Furthermore, Abu Daawood At-Tayaalisi narrated in his Musnad that ‘Ammaar said that Prophet said: "A cuckold will not enter Paradise." A cuckold is a man who approves indecency done by his womenfolk. So, what about a man who invites his wife to commit immorality?! For more information, please refer to Fatwa 82073.
At any rate, you should endeavor to look for a treatment, and if your wife agrees to remain with you and be patient regarding your current condition, then she may do so, and if she wishes to ask for a divorce, she may do so as long as she is harmed, and harm allows the wife to seek divorce. For more information, please refer to Fatwa 131953.
Allaah Knows best.