In this case use the formula for electric field at a distance x on the axis of a ring which is given by
E = Q x / 4pe0 (x2 + r2)3/2 .
The total electric field is the simple sum of electric fields due to positive and negative charges.
Er = Q x /4pe0 (x2 + r2)3/2+ Q (d - x) /4pe0 ((d - x)2 + r2)3/2