How to color a tag in a math equation?

\documentclass{article}
\usepackage{amsmath,amssymb}

\usepackage{mathtools}
\usepackage{xcolor}
\newtagform{red}{\color{red}(}{)}
\usetagform{red}
\begin{document}

\begin{align*}
   \color{red} \sum_{n=1}^\infty\dfrac{1}{n^2}=\dfrac{\pi^2}{6}.\tag{E1}
\end{align*}


\end{document}

You can redefine the tag

Hope this helps!

CODE with newcommand

\documentclass{article}
\usepackage{amsmath,amssymb}
\usepackage{xcolor}
\newcommand{\TAG}[1]{\tag*{\textcolor{red}{(#1)}}}
\begin{document}

This is my favorite equality:
\begin{align*}
    \color{red}\sum_{n=1}^\infty\dfrac{1}{n^2}=\dfrac{\pi^2}{6}.\TAG{E1}
\end{align*}

\end{document}

CODE based on the comments by daleif and Mico

\documentclass{article}
\usepackage{amsmath,amssymb}
\usepackage{xcolor}

\begin{document}

This is my favorite equality:
\begin{align*}
\color{red}\sum_{n=1}^\infty\dfrac{1}{n^2}=\dfrac{\pi^2}{6}.
\tag*{\textcolor{red}{(E1)}}
\end{align*}

\end{document}