This is an oft repeated factoid with lots of variations (my favorite is the tale that Tolkien's editor underlined "dwarves" and corrected it to "dwarfs" citing the OED. Upon seeing this correction, Tolkien allegedly replied "I wrote the OED, and I said dwarves"). This link seems to be a good resource in explaining the reality behind the difference: he was writing a lot very quickly, and made a mistake based in familiarity of plurals rather than philology or linguistics.

Plural elves has been the standard before Tolkien: https://www.websters1913.com/words/Elf

As for dwarves, this is what Wikipedia has to say, with reference to P. Gilliver et al. The Ring of Words: Tolkien and the Oxford English Dictionary:

Modern English has two plurals for the word dwarf: dwarfs and dwarves. Dwarfs remains the most commonly employed plural. The minority plural dwarves was recorded as early as 1818. However, it was later popularized by the fiction of philologist and legendarium author J. R. R. Tolkien, originating as a hypercorrective mistake. It was employed by Tolkien for some time before 1917.[6] Regarding his use of this plural, Tolkien wrote in 1937, "I am afraid it is just a piece of private bad grammar, rather shocking in a philologist; but I shall have to go with it."[6]

Doubt his publication would survive peer review.