The printer (For example Dymo 450 turbo) would print a label that matches the EAN
code. (The label is not a copy of the EAN code, it is a custom text. Each
EAN code has its own text label.)
The assembly doesn't really matter. The only requirement is a label printer & a barcode reader.
Also computer with linux / windows fits. No need to be an Arduino.
Dymo is in fact pretty easy, as they publish a no charge API for Windows.
Also their Labelwriters appear as standard Windows printers... just render the page as you want it and ‘print’