Like this? (The showframe
package is only to show the alignment, just remove it for production run)
The flushleft
or flushright
environments introduce some vertical spacing each time, this is cause for the two different lines!
Use \hfill
for easy cases, or a tabular, for more complicated setups, (i.e. line wrapping etc., which is quite likely if 'sentences' are to be used instead of short words)
\documentclass{article}
\usepackage{showframe}
\begin{document}
\noindent
\textbf{text1}
\hfill
\textbf{text2}
\end{document}

Update, with some wrapping for sentences
\documentclass{article}
\usepackage{tabularx}
\usepackage{ragged2e}
\usepackage{showframe}
\usepackage{array}
\newcolumntype{Y}{>{\RaggedLeft\arraybackslash}X}
\newcommand{\sentenceleftright}[2]{%
\begin{tabularx}{\textwidth}{@{}X@{}c@{}Y@{}}
#1 & & #2\\
\end{tabularx}%
}
\begin{document}
\parindent=0em
\textbf{text1}
\hfill
\textbf{text2}
\sentenceleftright{left}{right}
\sentenceleftright{And now (at last but not least) for something}{really really really really completely different}
\end{document}

text1 \hfill text2
... – Zarko Jun 4 '16 at 13:05