From Tolkien Gateway
Eldest was a title for the eldest of all beings. Confusingly, it seems to apply to two different individuals; not only does Tom Bombadil claim it for himself, but Celeborn also uses it to address the old Ent Treebeard. Tom Bombadil's nature, including what manner of being he is and if he can be considered alive and incarnate, remains unknown. The matter of who is truly the eldest living being in Middle-earth is a mystery.