If all the transactional activity that's occurred since the database dump is still in the transaction log, then yes you could do a dump tran and get your other database up to date by applying the database dump (from 10 days ago) and the tran log dump you just took.
If however the transaction log has been truncated at any point during the last 10 days (ie, transactions have been discarded), then you'll need to take perform a new dump database and then load the resulting dump file into your target dataserver.
'transactions have been discarded' means a) someone has issued a dump tran with {truncate_only|no_log} or b) someone issued a dump tran ... to <file> but said dump file has been lost/misplaced/deleted or c) the database has the trunc log on chkpt option set (which means the log is truncated each time the database is checkpointed (which happens throughout the day).
So, if you can account for all transactional activity since that database dump (10 days ago), then yes you can load the db dump plus a new tran log dump ... otherwise you'll need to take a new database dump.