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Although the other specialist may be right, you can still try; the hardest part will be finding a car that you want to rent nearby first.
AT 18, you are legally able to enter into a binding contract in most states, and you will need a credit card to process the transaction (a requirement ant all rental companies I have ever come across). Insurance may be a problem for someone your age though...
Why not consider hiring a limo instead? If you split the cost with a couple other friends it would probably not be all that expensive, and then you won't have to worry about damage, cleaning it, mileage charges, or traffic. You can all just relax and enjoy the evening then!