You can achieve the desired result in many ways. Below there's one such possibility; I assumed the sectional unit used was \chapter:
\documentclass{memoir}
% redefinition for the ToC title
\renewcommand\printtoctitle[1]{\HUGE\sffamily#1}
% redefinitions for chapter entries
\renewcommand\chapternumberline[1]{}
\renewcommand\cftchapterfont{\sffamily}
\renewcommand\cftchapterpagefont{\huge\sffamily}
\makeatletter
\newcommand\l@mychap[3]{%
\vskip2ex%
\par\noindent
\parbox{2.5em}{%
\hfill{\cftchapterpagefont#2}%
}\hspace*{3em}%
\parbox{\dimexpr\textwidth-5.5em-15pt\relax}{%
\cftchapterfont#1%
}\par%
}
\renewcommand*\l@chapter[2]{%
\l@mychap{#1}{#2}{\chaptername}%
}
\makeatother
\begin{document}
\tableofcontents*
\chapter{Down the Rabbit Hole}
\chapter{The Pool of Tears}
\chapter{The Caucus Race and a Long Tale}
\setcounter{page}{14}% just for the example
\end{document}

The code above will align the page numbers to the right; to get them aligned to the left, \l@mychap must be defined using something like
\newcommand\l@mychap[3]{%
\vskip2ex%
\par\noindent
\parbox{4.5em}{%
{\cftchapterpagefont#2}\hfill%
}%
\parbox{\dimexpr\textwidth-4.5em-15pt\relax}{%
\cftchapterfont#1%
}\par%
}
Using this redefinition (in the full example code above) instead of the initial one, one obtains
