voltage source= 20V

R1= 5 ohms
R2= 5 ohms
R3= 5 ohms

Find the Thevenin equivalent circuit for the network external to the resistor R

I have replaced R with an open circuit and so the voltage between the open circuit is 10V. Don't know how to go about from there.

 

So you find Vth, Next you need to find Rth.
Simply short E1 and find resistance seen from resistor R terminals.

 

Why is it that we have to short E1 though?

 

Because we need to find equivalent resistance without any source . And in the theory voltage source has a 0ohm internal resistance (act just like a short).