From the confidence interval
\begin{equation*}
P( \tilde{p} - z_{ \alpha/2}\sqrt{\tilde{p}(1-\tilde{p})/n} \lt p \lt \tilde{p} + z_{ \alpha/2}\sqrt{\tilde{p}(1-\tilde{p})/n}) = 1 - \alpha,
\end{equation*}
note that
\begin{equation*}
E = z_{ \alpha/2}\sqrt{\tilde{p}(1-\tilde{p})/n}.
\end{equation*}
Presuming E is given and n is unknown, simply solve for n (noting that n is an integer and therefore you will likely need to replace the equality with an appropriate inequality).