Who sent “the paper over the mail” and what is it, exactly?
If it’s a citation, then you may need to go to court to have a hearing on the matter. (And if you go to court and the complaining party doesn’t show up, then the whole thing should be thrown out of court.)
Otherwise, the advice so far is good, especially that from @Austinlad I think: have your facts bulleted and DO NOT get emotional about this. Even if you’re found guilty somehow, keep in mind that you did hit (when you rear-end someone it is always your fault for following too closely and failing to stop in time) and you did ‘run’, without making your own report to the police. So if you state all of the facts, that there was actual contact and there was no call to the police, you could be found guilty (and you would be incriminating yourself) even without any other testimony. Don’t incriminate yourself.
I would hedge the statement that you make: say that “you thought” there was contact, and that’s why you stopped to look at your vehicle. (It’s not lying to say that you “thought” there was contact. If you slam into him at 90 mph then “I think” there would be contact.) When you stopped (and I presume traffic still wasn’t moving fast), you could see that there was no evidence of collision on the vehicle in front (if that’s true) and no evidence on your vehicle, either (if that’s true).
At that point, and without the driver or owner of the struck vehicle coming forward, you should be in the clear. No one else witnessed “the event” except you and the vehicle in front of you, and the one who complained just saw what “he thought” was a hit-and-run. (And he was doing a good thing, himself, in reporting that. So if he does appear, then it would not be amiss to congratulate him for being a good citizen in reporting… and then showing up in court to follow through.) But if he wasn’t hit or didn’t see an actual collision, then his testimony after that is worthless.