How can achieve custom theorem environment where the title spans two lines? (preferably with tcolorbox)

Question

I'm already using tcolorbox for my theorems, so a solution based on that package would be ideal.

This is more or less what I had in mind:

EDIT: Just to clarify, the two lines of text beside the title are not independent from the rest. Everything from the lipsum is the content of the theorem.

EDIT 2: I updated the example to reflect how I would like the title to appear. It should read "this is the example's title", I got confused!

Answer 1

Here is a solution with ntheorem. I define a wrap theorem style, which simply uses \hangindent and \hangafter:

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage[thmmarks, amsmath, thref]{ntheorem}

\makeatletter
\newlength{\wrapboxlg}
\newtheoremstyle{wrap}%%
  {\item[\hskip\labelsep\Large\theorem@headerfont ##1~##2\theorem@separator]
\mbox{}\endgraf\settowidth{\wrapboxlg}{\Large\theorem@headerfont ##1~##2\theorem@separator\normalsize\enspace}
   \vskip-1.5\baselineskip
\hangindent = \wrapboxlg\hangafter =-2\noindent
}%
{\item[\hskip\labelsep\Large\theorem@headerfont ##1~##2]
\mbox{}\endgraf\settowidth{\wrapboxlg}{\Large\theorem@headerfont ##1~##2\theorem@separator\normalsize\enspace}
   \vskip-1.5\baselineskip
\hangindent = \wrapboxlg\hangafter =-2\noindent
 {\theorem@headerfont (##3)\theorem@separator}\ }%
 \makeatother

 \theoremstyle{wrap}
 \theoremheaderfont{\upshape\bfseries}
 \theorembodyfont{\normalfont}
 \theoremseparator{.}
 \newtheorem{Ex}{Example}[section]
\usepackage{lipsum}

\begin{document}

\setcounter{section}{1}
\setcounter{Ex}{22}

\begin{Ex}
    \lipsum[11]
\end{Ex}
\bigskip

\begin{Ex}[This is the example title]
    Sed feugiat. Cum sociis natoque penatibus et magnis dis par-
    turient montes, nascetur ridiculus mus. Ut pellentesque augue
    sed urna. Vestibulum diam eros, fringilla et, consectetuer eu, nonummy id,
    sapien. Nullam at lectus. In sagittis ultrices mauris. Curabitur malesuada
    erat sit amet massa. Fusce blandit. Aliquam erat volutpat. Aliquam euismod.
    Aenean vel lectus. Nunc imperdiet justo nec dolor.
\end{Ex}

 \end{document}