The ten tribes will not return [to the Land of Israel], for it is said: "The Lord . . . will cast them into another land, like this day" (Deut. 29:27). Just as this day goes and does not return, so the ten tribes who have gone will not return. Such is the opinion of R. Akiva. But R. Eliezer said: Scripture's saying "like this day" implies that just as the day grows dark and then grows light again, so, too, after darkness has fallen upon the ten tribes, light shall shine for them hereafter.
The two Rabbis are writing hundreds of years after the exile of the 9 tribes so their positions reflect different attitudes not an attempt to discuss reality. Rabbi Akiva was realistic. He knew that the members of the tribes had completely assimilated as Jews and could not be found. Just as the Rabbis got rid of the rules against converting certain tribes like the Moabite men by saying we could not determine who was a Moabite since the older nations were completely intermixed and no longer had separate identities.
Rabbi Eliezer, on the other hand, may have believed that there was something built into the souls of Jews that was permanent. This would allow G!d to bring them back no matter how assimilated they were.
I admit that Rabbi Akiva's position seems much more realistic, certainly today when it is thousands of years later. But when I meet converts who discover after converting that in fact they had Jewish ancestors, it sure raises some questions about the idea of a Jewish soul.