DC Circuit problem, an idea to solve this circuit?
One way to go about solving circuits with switches is looking at the circuit with the switch on and off. Use superposition. Pretend like your working with two different circuits. 

Solve the circuit with the switch off (no current will flow through R so you can remove (or ignore elements R and E)) You will end up with a capacitor that is charging up so for the first circuit you will have a circuit with initial conditions and a steady state (meaning after the capacitor is fully charged.

Then you have the other circuit with the switch on, you need to solve it with the cap fully charged for initial conditions of the second circuit, which was the steady state conditions of the first. I'll repeat that again, the cap will charge with the switch off, it will then have a voltage on it, the switch will turn on and then it will reach a different voltage value. 

This is a great exercise because it wraps your mind around two different concepts at the same time and if studied enough should leave you with an intuitive feel for time varying circuits. Learn onward...