Não, isso nunca é discutido em detalhes
Gandalf nos conta no início de Fellowship apenas que o espírito de Sauron "fugiu" (ênfase minha):
Isildur Elendil’s son cut the Ring from Sauron’s hand and took it for his own. Then Sauron was vanquished and his spirit fled and was hidden for long years, until his shadow took shape again in Mirkwood.
Fellowship of the Ring Book I Chapter 2: "The Shadow of the Past"
Mas até onde ele foi especificamente , tudo o que nos é dito é uma linha em O Silmarillion (ênfase minha):
Then Sauron was for that time vanquished, and he forsook his body, and his spirit fled far away and hid in waste places; and he took no visible shape again for many long years.
The Silmarillion V Of the Rings of Power and the Third Age