Gare de l'Est is very close to Paris Gare du Nord, so you could walk – it takes about 10 minutes.
Otherwise, buy a t+ ticket and take Métro Line 4 in the direction of Châtelet and get off the train at Gare de l’Est.
Follow signs to the TGV platforms and board a connecting train.
How to get back from Gare de l'Est to Paris Gare du Nord
Gare de l'Est is very close to Paris Gare du Nord, so you could walk – it takes about 10 minutes.
Otherwise, buy a t+ ticket and take Métro Line 4 in the direction of Porte de Clignancourt.
Get off the train at Paris Gare du Nord.
Approximate Métro journey time: 15 minutes
Approximate taxi journey time: 5 minutes