documentclass{article}
usepackage{amsmath}
begin{document}
begin{align} % bad spacing at first row, but correctly placed second row
    2 cosh t =& e^t \
            &+ e^{-t}
end{align}
begin{align} % good spacing at first row, but incorrectly placed second row
    2cosh t &= e^t \
            &+ e^{-t}
end{align}
end{document}

documentclass{article}
usepackage{amsmath}
begin{document}
begin{align}
    2 cosh t &= e^t \
              &quad+ e^{-t}
end{align}
end{document}

documentclass{article}
usepackage{amsmath}
begin{document}

noindent
The plus is flush with $e^t$ (I wouldn't recommend it):
begin{align}
2cosh t ={}& e^t \
            & negmedspace+ e^{-t}
end{align}
The plus is moved right (better):
begin{align}
2cosh t &= e^t \
         &qquad+ e^{-t}
end{align}
end{document}

documentclass{article}
usepackage{amsmath}
begin{document}

begin{equation}
begin{split}
2cosh t &= e^t \
         &qquad + e^{-t}
end{split}
end{equation}

documentclass{article}
usepackage{amsmath}
setlengthtextwidth{3in} %% just for this example
begin{document}
begin{align}
    2cosh t &= phantom{{}+{}} mathrm{e}^t \
             &phantom{{}={}} + mathrm{e}^{-t}
end{align}
end{document}

documentclass{article}

usepackage{amsmath}

begin{document}

begin{align}
   2cosh t
   &= e^{t} \
   &hphantom{{}=} + e^{-t}
end{align}

end{document}

2 cosh t & ; mathord{=} ; e^t \
          & ; phantom{=} ; mathord{+} : e^{-t}

2 cosh t & = e^{t} \
          & mathrel{phantom{=}} negmedspace {} + e^{-t}