If you registered your Elements with an AdobeID then will have a record of the serial number that you can see by logging in with the AdobeID you registered the product using, click on manage account and then Plans and Products across the top. I think the 9 digit number is just some printing sequence for the label or maybe a product number so won't do you any good.

A PSE serial number is 6 groups of 4 digits with the first four digits being 1057.