We prove the Tits-Weiss conjecture for Albert division algebras over fields of arbitrary characteristic in the affirmative. The conjecture predicts that every norm similarity of an Albert division algebra is a product of a scalar homothety andUU-operators. This conjecture is equivalent to the Kneser-Tits conjecture for simple, simply connected algebraic groups with Tits indexE8,278E^{78}_{8,2}. We prove that a simple, simply connected algebraic group with Tits indexE8,278E_{8,2}^{78}orE7,178E_{7,1}^{78}, defined over a field of arbitrary characteristic, isRR-trivial, in the sense of Manin, thereby proving the Kneser-Tits conjecture for such groups. The Tits-Weiss conjecture follows as a consequence.