If you make successful the energy bar of the Eye of Sauron empty in the fight, then for a short time it seems that Sauron is weakening. But then, he heal himself immediately. Talion and Celebrimbor realize that they can't defeat Sauron, because the destruction of the One Ring is the only way to defeat him forever. Celebrimbor know a way that he and Talion can escape from a definitive dead in Sauron's hands, with teleportation. But Celebrimbor has on that moment only enough power to teleport only one (Talion or himself). After all what Talion and Celebrimbor have experienced together in Mordor, their friendship is grown so strong. Celebrimbor choose to teleport Talion, and after that, Sauron destroy Celebrimbor, without hesitation. On the place where Talion is teleport, Talion mourning for the loss of his partner, and friend. Then, Talion realize that Celebrimbor's last wish would be that Sauron will be stoped. But he know that he can't do that alone any longer (no wraith powers anymore), and that Sauron's armies will looking for him, after all. Talion choose to change his identity and return to Gondor to join himself to the remaining Rangers. The rest of Talions path is unknown. Meanwhile, in Mordor, Sauron prepare his armies, and soon, the War of the Ring will begin.
Another end, close beside the canon end
If you are killed in the fight, Sauron start with his final strike. Talion and Celebrimbor can't escape, Celebrimbor don't have enough power on that moment. So, Sauron destroy both Talion and Celebrimbor, forever. Later, prepare his armies, and soon, the War of the Ring will begin.
The way to these two alternate endings
If you have acquired enough information about the One Ring before your meeting with Gollum, then you can dominate Gollum that he know the location of the Shire again from his old memory as the Stoorish Hobbit Sméagol, and then he to the Shire to find the One Ring and bring it to you. Then Gollum come back when the end of the game is close. If you have the One Ring before the confrontation with Sauron on the top of Barad-dûr, then instead of a fight against Sauron that Talion and Celebrimbor never will win for real, Sauron takes the One Ring and come back to his physical form. He will sarcastic thanks Talion and Celebrimbor (knowing that the body is shared by two separate souls) for bring the Ring back to him, indicate that he is impressed for actions of Talion and Celebrimbor in Mordor, and ask them instead to take revenge on him, join to his side. Talion and Celebrimbor refuse the offer. So Sauron challenge them for an final confrontation inside Mount Doom, a fight that will determine the fate of Middle-earth.
Bad alternate end (defeated by Sauron)
If you are killed in the fight, Sauron destroy both Talion and Celebrimbor, forever. Sauron brings his armies together and soon, he will dominate all of Middle-earth.
Good alternate end (defeating Sauron)
If you defeated Sauron in the fight successful, Tailon (with Celebrimbor's help) strikes Sauron into the Cracks of Doom. The fires of Mount Doom destroy both Sauron's body and the One Ring, Sauron is gone from Middle-earth, forever. Talion and Celebrimbor have got their revenge, and the destroyed threat that Sauron represented for Middle-earth. Celebrimbor bless Talion for a new good life in Middle-earth, and Celebrimbor can rest in peace. Then Talion leaves Mordor, seeking to his new good life.