LaTeX hanging paragraphs - latex

Question

I'd like to set up my paragraphs to hang only on the second line. The hanging environment will hang after a particular line, but not on a specific line.
To piggyback off of another question LaTeX: indent from second line, I want it to produce something like this:
Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Proin eu tempor velit. Fusce accumsan ultrices fringilla. Praesent
sed odio mi. Mauris non ligula turpis. Duis posuere lacus nec diam
interdum dictum suscipit magna molestie. Vestibulum nibh dolor,
interdum eget rhoncus ut, sodales eget justo. Morbi blandit lorem
sit amet nulla egestas aliquam. Nunc pharetra est at nibh ullamcorper
in commodo erat dignissim. Cras et suscipit enim.
Nunc adipiscing ligula at ligula egestas id ullamcorper felis luctus.
Aliquam tincidunt turpis sed eros pellentesque iaculis. Nulla
imperdiet cursus enim condimentum congue.
It would also be nice if this could be a set document wide instead of just an environment, but not necessary.
EDIT: Here is my best example of what each paragraph looks like.
\documentclass{article}
\begin{document}
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Proin eu tempor velit. Fusce accumsan ultrices fringilla. Praesent sed odio mi. Mauris non ligula turpis. Duis posuere lacus nec diam interdum dictum suscipit magna molestie. Vestibulum nibh dolor, interdum eget rhoncus ut, sodales eget justo. Morbi blandit lorem sit amet nulla egestas aliquam. Nunc pharetra est at nibh ullamcorper in commodo erat dignissim. Cras et suscipit enim.\\
Nunc adipiscing ligula at ligula egestas id ullamcorper felis luctus. Aliquam tincidunt turpis sed eros pellentesque iaculis. Nulla imperdiet cursus enim condimentum congue.\\
\end{document}

Answer 1

You can update \everypar to insert a specific \parshape. This should re-organize the flow to match your requirement:
\documentclass{article}
\usepackage{etoolbox,lipsum}
\newlength{\saveparindent}\setlength{\saveparindent}{\parindent}
\setlength{\parindent}{0pt}
\newcommand{\updateeverypar}{%
\parshape 3
0pt \linewidth
\saveparindent \dimexpr\linewidth-\saveparindent\relax
0pt \linewidth}
\makeatletter
\patchcmd{\#xsect}{\ignorespaces}{\ignorespaces\everypar{\updateeverypar}}{}{}
\makeatother
\AtBeginDocument{\everypar{\updateeverypar}}
\begin{document}
\lipsum[1]
\section{Introduction}
\lipsum[2-3]
\section{Conclusion}
\lipsum[4-5]
\end{document}
Note though that \everypar may be updated unexpectedly within standard document elements. See, for example, the spacing above 1 Introduction compared to that of 2 Conclusion. Depending on your application or usage, this might be a problem or not, and may require adjustments.