can I reauthorize a computer I accidentally deauthorized without having the computer with me? The computer I would like to authorize has been authorized under my account. Thank you!

I removed a computer from the authorization list accidentally. I would like to authorize the computer I accidentally removed, however, I do not have the computer with me to sign in and authorize the computer again. I am afraid I will have issues since the computer I removed from the authorization list is the computer I added all of the current music I own. My question in summary, is how do I (if possible) re-authorize the computer I removed from the authorized computers under my account, with out having access to that computer because it is at home and I am currently on a business trip. Any help would be greatly appreciated, and again, the computer I am trying to authorize, was authorized prior to accidentally removing it from my authorized computers. Thank you!