Matt-B is correct. If you do not have a copy of the deleted notes somewhere else, it is gone.
As for restoring via an iCloud backup, that does not help in this matter. "Your iOS device backup only includes data and settings stored on your device. It doesn’t include data already stored in iCloud. That includes contacts, calendars, bookmarks, mail messages,
notes, shared photo albums, iCloud Photo Library, My Photo Stream, and documents you store in iCloud Drive."
Source:
https://support.apple.com/kb/PH12519?locale=en_US