[![documentclass[a4paper,symmetric,twoside,justified]{tufte-book}
usepackage{lipsum}
usepackage{graphicx}
usepackage{wrapfig}
usepackage{mdframed}
usepackage[many]{tcolorbox}
usepackage{xcolor}
definecolor{mycolor}{RGB}{0,125,98}
usetikzlibrary{calc}

tcbset{mystyle/.style={
  breakable,
  enhanced,
  outer arc=0pt,
  arc=0pt,
  colframe=mycolor,
  colback=mycolor!20,
  attach boxed title to top left,
  boxed title style={
    colback=blue,
    outer arc=0pt,
    arc=0pt,
    top=3pt,
    bottom=3pt,
    },
  fonttitle=sffamily
  }
}

newtcolorbox[auto counter,number within=section]{example}[1][]{
  mystyle,
  title=Example~thetcbcounter,
  overlay unbroken and first={
      path
        let
        p1=(title.north east),
        p2=(frame.north east)
        in
        node[anchor=west,font=sffamily,color=mycolor,text width=x2-x1]
        at (title.east) {#1};
  }
}

begin{document}
mainmatter
chapter{First chapter}

section{A section}

% example env
begin{example}[Example environment]

begin{wrapfigure}{r}{0.5textwidth}
rule{4cm}{2cm}
end{wrapfigure}

lipsum[1]
end{example}

% example using tufte's fullwidth
begin{fullwidth}
begin{example}[Example environment inside tufte's fullwidth]

begin{wrapfigure}{r}{0.5textwidth}
rule{4cm}{2cm}
end{wrapfigure}

lipsum[1-6]
end{example}
end{fullwidth}

end{document}][1]][1]