You just need to take the (simple) harmonic mean of the P/E's of the stocks in the index given that it's an equal-weighted equity index.
Suppose you have $N$ stocks in the equal-weighted index. Then, using the harmonic mean formula, the index's P/E would be calculated as:
$$\text{P/E}_{\text{index}} = \dfrac{N}{\mathop {\sum}\limits_{i=1}^{N}\frac{1}{\text{P/E}_i}} \tag{1}$$
where $\text{P/E}_i$ is the P/E of stock $i$ and calculated as $\frac{M_i}{E_i}$ with $M_i$ being the stock $i$'s market cap and $E_i$ its earnings.
The logic behind the use of the harmonic mean can be explained by using the holding company analogy which I also used in my answer to another question about index P/E's.
Suppose the assets of a holding company $H$, whose market cap is $R_H$, comprise of $N$ stocks with equal weights. The holding company's earnings, $E_H$, would then be the sum of the earnings of the stocks, $E_i$, weighted by the holding company's respective ownership ratios, $x_i$, in each. Then, the holding company's P/E would be:
$$\begin{align}
\text{P/E}_{H} &= \dfrac{R_H}{E_H} \\
&= \dfrac{R_H}{\mathop {\sum}\limits_{i=1}^{N}x_iE_i}.
\tag{2}
\end{align}$$
Assuming $M_i$ again denotes the market cap of the stock $i$, we can figure out $x_i$ as follows:
$$\begin{align}
x_iM_i &= \dfrac{R_H}{N} \\
x_i &= \dfrac{R_H}{NM_i}. \tag{3}
\end{align}$$
Substituting (3) into (2), we find:
$$\begin{align}
\text{P/E}_{H}
&= \dfrac{R_h}{\mathop {\sum}\limits_{i=1}^{N}\left(\dfrac{R_H}{NM_i}\right)E_i} \\
&= \dfrac{R_H}{\dfrac{R_H}{N} \mathop {\sum}\limits_{i=1}^{N}\left(\dfrac{1}{M_i}\right)E_i} \\
&= \dfrac{N}{\mathop {\sum}\limits_{i=1}^{N}\dfrac{E_i}{M_i}} \\
&= \dfrac{N}{\mathop {\sum}\limits_{i=1}^{N}\dfrac{1}{\frac{M_i}{E_i}}} \\
&= \dfrac{N}{\mathop {\sum}\limits_{i=1}^{N}\frac{1}{\text{P/E}_i}}
\tag{4}\end{align}$$
which is the same as the equation (1).
