The package times has been obsolete for several years; with it the math will still be typeset with Computer Modern that horribly clashes with Times New Roman.
Either use mathptmx or, much better, newtxtext and newtxmath.
However, it turns out that the Euler “w” is not very distinct from the Times italic ”w”, so perhaps you can use the bold version of the Euler letter.
\documentclass[a4paper,12pt]{book}
\usepackage[T1]{fontenc}
% for Times in text and math
\usepackage{newtxtext,newtxmath}
% or the following
%\usepackage{mathptmx}
\DeclareSymbolFont{eulerletters}{U}{zeur}{b}{n}
\DeclareMathSymbol{\eulw}{\mathord}{eulerletters}{`w}
\begin{document}
\[
\eulw_1 = ax + b - w
\]
\end{document}

This is how it would be with a medium Euler “w”, obtained by changing the code above in
\DeclareSymbolFont{eulerletters}{U}{zeur}{m}{n}

My opinion is that in both cases your readers will not appreciate the distinction.
Maybe using \mathsf{w} would be a better choice
\[
\mathsf{w}_1 = ax + b - w
\]
would produce

win math mode to be in the Euler font or just that one? – egreg Mar 24 '15 at 23:39times, butmathptmx, or the math symbols will be in the (non compatible) Computer Modern font. However, the Euler w is quite similar to the Times w, so your choice doesn't seem to be good. – egreg Mar 24 '15 at 23:52whas specific meaning, you should define a macro to be consistent. – Werner Mar 24 '15 at 23:54wrepresents (say) a vector and you want to denote vectors using a different font. Or, ifwrepresents (say) some "wacky constant", you may want to be consistent in its representation. – Werner Mar 25 '15 at 00:00\wordthat formats its argument accordingly. – Werner Mar 25 '15 at 00:06