Add vertically-aligned text between two enumerate items

How about a simple \raisebox, wrapped in a macro taking into account \itemsep and \parsep values (thanks to circumscribe, I have change to \glueexpr, since all involved lengths are glues, not ordinary lengths!)

\documentclass{article}

\usepackage{enumitem}

\newcommand{\raisecontent}[1]{%
  \raisebox{\glueexpr\baselineskip/2+\parsep/2+\itemsep/2+\lineskip/2}[\ht\strutbox][\ht\strutbox]{#1}%
}

\begin{document}
 \begin{enumerate}
  \item $Y^2 - 1 = 0$ 
  \item $Y^2 + 1 = 0$ \raisecontent{\quad (text)}
 \end{enumerate}

 \begin{enumerate}[itemsep=40pt]
  \item $Y^2 - 1 = 0$ 
  \item $Y^2 + 1 = 0$ \raisecontent{\quad (text)}
 \end{enumerate}

\end{document}

Another solution, based on tabularx and listliketab, which emulates list environments within tables:

\documentclass{article}
\usepackage{tabularx, listliketab, multirow}

\begin{document}

\storestyleof{enumerate}
\begin{listliketab}
\newcounter{tabenum}\setcounter{tabenum}{0}
\newcommand{\tabitem}{\addtocounter{tabenum}{1}\thetabenum.}
 \noindent\begin{tabularx}{\linewidth}{@{}L l@{\quad}X@{}}
  \tabitem & $Y^2 - 1 = 0$ & \multirow{2}{=}{(Text)}\\
  \tabitem & $Y^2 + 1 = 0$
 \end{tabularx}
 \end{listliketab}

\end{document}