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We know that many Ainur entered Eä at the beginning of time, the most powerful forming the Valar and the lesser the Maiar, but how many remained behind with Eru? Does Tolkien ever discuss this in any of his letters?
Tolkien wrote extremely little about the Timeless Halls in general, and most of what he did write only concerns the spirits who would go on to have interactions with Elves and Men.
We know nothing at all about the rest of them.
No, he did not write anything about them. The no of the Ainur who entered Arda is only known but not of ones left behind nor the total no of Ainur in the whole universe.
Required, but never shown