To typeset inline verbatim-like material, it's best to use the macros \verb and \Verb; the latter is provided by the fancyvrb package. If that package is loaded and the instruction \VerbatimFootnotes is executed, one can even have \Verb instructions in footnotes. (One can't do this with \verb.)
Note that \verb and \Verb don't use matching pairs of curly braces ({ and }) to delimit their arguments; instead, use any non-letter symbol (except "*") that doesn't occur in the verbatim material itself. (Even \verb{<p>{ is legal, though I'll be the first one to state that it looks positively weird.)
If you prefer to render the inline verbatim material using the "regular" text font instead of a monospaced font, consider loading the listings package and writing "Paragraph element \lstinline{<p>}".

\documentclass{article}
\usepackage{fancyvrb} % for "\Verb" macro
\VerbatimFootnotes % enable use of \Verb in footnotes
\setlength\textheight{3cm} % just for this example
\begin{document}
\obeylines
Paragraph element \verb+<p>+
Paragraph element \verb_</p>_
Paragraph element \Verb^<p>^
Paragraph element \Verb#</p>#
\VerbatimFootnotes
Some text.\footnote{In a footnote: \Verb"<p>", \Verb:</p>:.}
\end{document}
\verb!<p>!? There are also some packages that provide inline display for various programming languages , seelistingsorminted, for example – Aug 22 '17 at 16:56This is paragraph element \verb+<p>+."? Note the use of the delimiter+to start and terminate the inline verbatim material. The delimiter can be any symbol that doesn't occur in the verbatim material. – Mico Aug 22 '17 at 17:00verbatimwas the only way I could achieve this. Thanks. – denisr Aug 22 '17 at 17:01