You say they hit you, they say you hit them. Without 3rd party witnesses it comes down to he said she said. Unless you have proof such as video recording or something else you won't win this argument.
Actually your description of the damage would tend to lend more weight to the other drivers argument as they would have been in your blind spot while they should have been able to see you clearly. I'm not saying who hit who and I have Zero experience in accident reconstruction, but if I was asked to look at the damage alone without speaking to either driver I would tend to think the odds were leaning toward the fact that it was your fault.
So again without witnesses you're probably screwed.

