Why is \$E_1=\frac{F}{q}=\frac{K\frac{Q_1 Q_2}{x^2}}{Q_2}\$, instead of \$=\frac{K\frac{Q_1 Q_2}{x^2}}{Q_1}\$?
The first formula - the one which you do not agree with - can not be correct, since it has a wrong dimension -- assumed that K has the usual Am/Vs or m/F units. Also K can not be dimensionless.

I am also not 100% sure what is denoted by E_1. If it is the electric field at P due only to Q_1, than $$ E_1 = \frac 1 {4 \pi \epsilon_0} \frac {Q_1 Q_2} {x^2}$$. If you should consider the effect of Q_2, just use superposition.

PS: please avoid formulas in the title. It is hard to read and take some time to be rendered in the browser.