\documentclass[12pt]{report}
\usepackage{amsmath}
\begin{document}
\begin{align}
a & = a \\
f & =
\begin{cases}
a \\
b
\end{cases}
\end{align}
\newenvironment{foo}{}{}
\newenvironment{textequation} {$$\begin{foo}} {\end{foo}$$}
\Picture*{} \begin{textequation} a \end{textequation} \EndPicture
\begin{textequation} a \end{textequation}
\renewenvironment{textequation} {$$} {$$}
\Picture*{} \begin{textequation} a \end{textequation} \EndPicture
\begin{textequation} a \end{textequation}
\renewenvironment{textequation} {\begin{foo}\begin{foo}} {\end{foo}\end{foo}}
\Picture*{} \begin{textequation} a \end{textequation} \EndPicture
\begin{textequation} a \end{textequation}
\renewenvironment{textequation} {\begin{foo}} {\end{foo}}
\Picture*{} \begin{textequation} a \end{textequation} \EndPicture
\begin{textequation} a \end{textequation}
\ConfigureEnv{textequation} {\Picture*{}} {\EndPicture} {}{}
\Picture*{} \begin{textequation} a \end{textequation} \EndPicture
\begin{textequation} a \end{textequation}
xxxxxxx
\begin{equation}
g(E) =
\end{equation}
yyyyyyyy
\end{document}