This a an AU story so things fit nicely 
Reborn as an immortal Elf in Middle-earth, Edward Elric must wield his genius, his courage, and his heart to reshape a world of magic, war, and destiny — and find the love that was always meant for him.

When a golden-haired Elf-child is found in Rohan, the princess raises him as her son. But at three, he remembers his past life as Edward Elric, a prodigious alchemist from another world. Gifted, stubborn, and brilliant, Edward grows to challenge the traditions of Men and Elves alike — and his fate will eventually intertwine with Arwen Undómiel, forging a legend across the ages.
Disclaimer:
The Golden Child is a work of fanfiction. All characters, settings, and elements from Middle-earth, as well as Edward Elric from Fullmetal Alchemist, belong to their respective creators. This story is an original reinterpretation and is not intended for commercial use. Events, relationships, and characterizations in this work are fictional and may differ significantly from canon.

Chapter 20 - update