Now, this is the equation for the electric field of a ring of charge in the yz plane centered at the origin. We have a choice: to place the second ring at x = R or to center the rings at x = +/- R/2. I'm going to go with the more symmetrical +/-R. I'm also going to assume that both rings have the same signed charge. That is to say I'm assuming both rings have charge +q.
The field of the ring at x = -R/2 will be the ring of charge equation translated by R/2:
Likewise for the ring at x = +R/2:
So do you put these together? (Remember that E is a vector.)