Disclaimer This is a way to go but please don't do that since the output is not really reader-friendly.
If you do not want to modify anything else in the section titles style, you can add the following code
\documentclass{article}
\usepackage{blindtext}
\usepackage{hyperref}
\makeatletter
\newcommand\gobblepars{%
\@ifnextchar\par%
{\expandafter\gobblepars\@gobble}%
{}}
\makeatother
\newenvironment{mysec}[1]{%
\stepcounter{section}%
{\bfseries\noindent\thesection\hspace{0.5em} #1\hspace{0.5em}}%
\addcontentsline{toc}{section}{\thesection \hspace{0.5em} #1}%
\sectionmark{#1}}%
{\gobblepars \hspace{0.5em}}
\begin{document}
\begin{mysec}{First Section Title}
\blindtext
\end{mysec}
\begin{mysec}{Second Section Title}
\blindtext
\end{mysec}
\end{document}
The gobblepars
command is coming from this answer.
You will get this kind of output

NOTE I am not entirely sure about the part for the sectionmark
and all kind of advise would be welcomed. Concerning the TOC it seems to work properly as well as the section numbers.