Voltage calculation with the nodal analysis
simulate this circuit &ndash; Schematic created using CircuitLab

Node 0 is your reference.

$$\frac{e_1-v_e}{R_1}+\frac{e_1}{R_2}+\frac{e_1-e_3}{R_3}=0$$ 

Node 2, there is no need for KCL because of the voltage source.

$$e_2 = v_e$$ 

Node 3.

$$\frac{e_3-e_1}{R_3} + \frac{e_3 - v_e}{R_4}=0$$ 

Two equations, two unknowns.

Assume unknown currents leave node.