In S1E5 of The Rings of Power, King Gil-galad and Elrond tell a story about an elf and a balrog fighting over a tree on top of a mountain as they tell the backstory about the origin of mithril. They mentioned the light of The Silmarils.
Gil-galad: Are you familiar with The Song of the Roots of Hithaeglir?
[...]
Elrond: An obscure legend regarded by most to be apocryphal.
[...]
Elrond: It speaks of a battle, high among the peaks of the Misty Mountains. Not over honor or duty. But over a tree. Within which some claim was hidden the last of the lost Silmarils.
On one side, fought an Elven warrior, with a heart as pure as Manwë, who poured all of his light into the tree to protect it. On the other, a Balrog of Morgoth, who channeled all his hatred into the tree to destroy it. Amidst their duel unending, lightning ensnared the tree... Forging of their conflict, a power...
Gil-galad: A power as pure and light as good. As strong and unyielding as evil. They say it seeped down the roots into the mountain depths, where for centuries now, it has waited.
[...]
Gil-galad: The ore containing the light of the lost Silmaril.
What was the significance of that tree? Who was that elf?
Is that story hinted at in any of the texts?