Using biblatex instead of the journal's bst-based style probably isn't a good idea. That said none of the standard or contributed biblatex styles will give you this output. The document below demonstrates how you can obtain a custom style based on standard variants of numeric and authoryear.
\documentclass{article}
\usepackage{csquotes}
\usepackage[american]{babel}
\usepackage[citestyle=numeric,bibstyle=authoryear,sorting=none,
firstinits,terseinits,dashed=false]{biblatex}
\usepackage[colorlinks]{hyperref}
% Name list format
\renewcommand*{\labelnamepunct}{\addspace}
\renewcommand*{\finalnamedelim}{%
\ifbibliography{\addcomma\space}{\addspace\&\space}}
\renewcommand*{\revsdnamepunct}{}
\DeclareNameAlias{sortname}{last-first}
% No quotes or italics in titles
\DeclareFieldFormat{title}{#1}
\DeclareFieldFormat[article,inbook,incollection,inproceedings,patent,
thesis,unpublished]{title}{#1}
\DeclareFieldFormat{journaltitle}{#1}
\DeclareFieldFormat{issuetitle}{#1}
\DeclareFieldFormat{maintitle}{#1}
\renewbibmacro*{in:}{%
\ifentrytype{article}{}{\printtext{\bibstring{in}\intitlepunct}}}
% Remove page prefixes
\DeclareFieldFormat{pages}{#1}
% Only print journal volume
\renewbibmacro*{volume+number+eid}{%
\setunit*{\addspace}%
\printfield{volume}}
% Use colon for volume-pages delimiter
\renewcommand*{\bibpagespunct}{%
\ifentrytype{article}{\addcolon\space}{\addcomma\space}}
% Add labelnumbers to bibliography
\DeclareFieldFormat{labelnumberwidth}{#1\adddot}
\defbibenvironment{bibliography}
{\list
{\printtext[labelnumberwidth]{%
\printfield{prefixnumber}%
\printfield{labelnumber}}}
{\setlength{\labelwidth}{\labelnumberwidth}%
\setlength{\leftmargin}{\labelwidth}%
\setlength{\labelsep}{\biblabelsep}%
\addtolength{\leftmargin}{\labelsep}%
\setlength{\itemsep}{\bibitemsep}%
\setlength{\parsep}{\bibparsep}}%
\renewcommand*{\makelabel}[1]{\hss##1}}
{\endlist}
{\item}
% Omit authoryear disambiguation
\AtEveryBibitem{\clearfield{extrayear}}
\begin{filecontents}{\jobname.bib}
@article{glashow,
author = {Glashow, Sheldon},
title = {Partial symmetries of weak interactions},
journaltitle = {Nucl~Phys},
volume = {22},
date = {1961},
pages = {579--588}}
@article{weinberg,
author = {Weinberg, Steven},
title = {A model of leptons},
journaltitle = {Phys~Rev~Lett},
volume = {19},
date = {1967},
pages = {1264--1266}}
@book{companion,
author = {Goossens, Michel and Mittelbach, Frank and Samarin, Alexander},
title = {The LaTeX Companion},
edition = {1},
publisher = {Addison-Wesley},
location = {Reading MA},
date = {1994},
pagetotal = {528}}
\end{filecontents}
\addbibresource{\jobname.bib}
\begin{document}
\textcite{weinberg,glashow,companion}
\printbibliography
\end{document}

Some notes:
- The default
\revsdnamepunct corresponds to the comma printed between the last and first parts in a reversed name. It was introduced in 2.2. For older biblatex versions refer to this previous answer from lockstep.
- You can format titles to sentence case. Refer to this post for details.
- Journal title abbreviations might be better handled using the
string entry type. Refer to the bib file in the biblatex documentation for some examples.