Not two souls. RJ confirmed that Rand and LTT are quite literally the exact same soul. So one soul and two distinct and separate personalities of that soul. At the end of TGS, Rand finally integrates and accepts this fact and this causes LTT to "merge" with him. Beyond that we don't know until the next book, though most expect that Rand will have access to LTT's memories now.

I don't recall RJ every saying they were separate ... for some reason I thought he had given us an Aes Sedai answer when asked