Unlike the VW or Skoda units. The serial numbers are not printed on the sticker. Without power you cannot see the SN anywhere.
There are mainly three kinds of methods to find the serial numbers for Audi RNS-E systems:
I. Displayed on code entry screen:
If you are running US SW 0260 the number is shown in the code entry screen. Otherwise everybody with a VAG-COM cable or the dealer can read out the serial number via diagnostics. That's of course assuming that there is a valid serial number stored on your RNS-E main board (which is sometimes not the case for units from Eastern European sources).
II. Engineering mode for Audi Navigation+ RNS-E:
If the code has been entered already you can see the SN in engineering mode.
1) Turn on RNS-E.
2) Press the NAV button and release. (wait 5-10 seconds)
3) Press the top-left cursor button (around dial) for 5 seconds & release. (the indicator light stays on to acknowledge it's been long enough)
4) Press the top-right cursor button for 5 seconds. Hold until the screen changes.
"It doesn't mean the << >> Arrow keys, it means the top left and right soft buttons around the dial. "
III. Rose-Tech VAG-COM cable:
In VAG-COM, open module #56 and press the Advance ID (1A) button. The serial number is listed as one of the values there. Learn more about VAG-COM.