Can I go to Andorra for few days while visiting Barcelona with a multi entry tourist Schengen visa issued from the embassy of Spain in Egypt? Or do I need a letter?
Andorra has stayed outside the Schengen Agreement and maintains border controls with the EU. However as travellers to Andorra have to pass through the Schengen Area, and Andorra does not issue any visas, but accepts Schengen visas, Andorra is in practice a virtual part of the area. Third country nationals wishing to visit Andorra need a multi-entry Schengen visa, since to leave Andorra they must enter the Schengen area a second time.
So in short, yes, your multi-entry Schengen visa should be sufficient to enter Andorra and then to leave Andorra, re-entering the Schengen area.