Is it possible that a duplicate Earth is located exactly across the other side of the Sun? If they rotate the same amount of 24 hours a day, we would never see it because we would always be on the opposite sides of the sun.
No. We've sent probes to other planets and they have looked back to Earth. If there were a second Earth in our orbit, those probes would have seen both Earths.
Technology nowadays is way beyond such myths. When we can draw the whole map of the solar system and observe even the tiniest of asteroids, how could it be possible to miss such a gigantic body alike the Earth.