I'm not 100% sure of your issue - are you trying to find your printers ePrint address? If so, it should be a 12 character alpha-numeric string with @hpeprint.com at the end of it - you can find it within your ePrint Web Services menu onboard your ePrint enabled printer.
It is worth pointing out, that this string can be renamed to a string of your choice within your online eprintcenter.com account - once your choice is still available.
Thank you! I think the trouble was something faulty with my registration on HP site, I tried again and was able to login successfully (after several invalid ID attempts) and the email came up fine and I was able to change it to something that will stick in my head.