Is this for SQL Server 2000?
You have a couple of options if you don’t want to replace all the data in your database. You could restore your backup to a new database and export only the missing table to its original database. You could also restore a specific transaction log if you back those up regularly, but that would roll back all transactions since the backup to that point.
As for tracking the machine where deletion command came from, that is more difficult. If you have audit logging enabled, you’ll be able to view the logs and see who was logged in at the time. You won’t be able to see the details of individual commands unless you were performing a trace at the time which captured the machine name, login name, sql command, etc.
Hope this helps,