The simplest way to transfer between Gare du Nord and Gare de l'Est is on foot.
You can take the metro but the one stop journey isn't
worth it. Walk out of the front of the station on to Rue de Dunkerque. Turn left along to the crossing in front of the
glassed fronted section of the station and cross over onto Rue de St.Quentin. Continue down the street until it meets Boulevard de Magenta, turn left onto the street and carry on until the first major junction. You now want to turn onto Rue du 8 Mai 1945 which will eventually lead you to the front of Gare de l'Est
View Gare du Nord to Gare de L'st in a larger map
If you do not want to take the walk you are only one stop away on line
of the metro system