score:10
You cannot get an NIE unless you are a resident of Spain, so forget about it for your 10 day trip. As part of the application process, you will have to show a certificado de empadronamiento, which is a document from your local Spanish town hall showing that you actually live there.
Getting an NIE isn't a particularly easy or quick process, and requires documentation, visits to multiple municipal offices, and a not insignificant amount of time waiting in line. Even if you could get one, it almost certianly wouldn't be worth it to potentially save some money on a speeding ticket.