{ corresponds to \bgroup
} corresponds to \egroup
However, the problem with using braces is that doing
constructs like
{a}
{b}
introduce, often unexpected and unwanted, spaces between the
a and b. The \bgroup \egroup forms don't have this problem.
Anyway, the left shift of the numbers I think is due to
algorithm2e's patching into the paragraph system.
In any case, it is best you use a macro to define such
special contructs so you only have one place to change
it as need be.
Try this and see how you like it:
\documentclass[12pt, oneside]{book}
\usepackage{lipsum} %remove \lipsum[#]
%ALGORITHM CODE
\usepackage[linesnumbered,ruled]{algorithm2e}
%-----------------------------BEGIN-----------------------------
\begin{document}
\newcommand{\MYalgopar}[1]{\bgroup
\parindent 0pt
\leftskip 5pt
\par\textbf{Start}:\par
\bgroup\everypar={\nl\hspace{5pt}\relax}\leftskip 15pt\relax
#1\egroup\textbf{End}\par\egroup}
\begin{algorithm}[H]
\SetKwInOut{Input}{Input}
\SetKwInOut{Output}{Output}
\SetKwInOut{Define}{Define}
\underline{Initialise:} Conditions for Algorithm\;
\Define{define functions for algorithm}
\Input{input of algoithm}
\Output{Output}
\underline{Run through algorithm In Full:}
\MYalgopar{\lipsum[1]}
\caption{Name of algoithm and details etc...}
\end{algorithm}
\end{document}
It will handle multiple paragraphs as well:
\MYalgopar{\lipsum[1]\par\lipsum[1]}
Cheers,
Mike