How to enumerate just one line in align environment

I would like to suggest that you nest an aligned environment inside an equation environment. That way, if you ever decide that you would prefer to place the equation number at the bottom instead of at the top, all you'd have to change is replace begin{aligned}[t] with begin{aligned}[b].

I would also like to suggest you load the mathtools package and use its smashoperator macro to tighten up the spacing around some of the sum terms.

documentclass{article}
usepackage{mathtools,amssymb}
usepackage{newtxtext,newtxmath} %optional (Times Roman font)
begin{document}
begin{equation}label{computation-one}
begin{aligned}[t]
&langle tilde{overline{nabla}}_{!tilde{e}_i}  
         tilde{mathbf{S}}, tilde{e}_j rangle^2 
+langle tilde{overline{nabla}}_{!e^{-f}!tilde{e}_0} 
    tilde{mathbf{S}}, e^{-f}!tilde{e}_0 rangle^2 
+ sum_{i=1}^n tilde{R}
  (tilde{e}_i, tilde{mathbf{S}}, tilde{mathbf{S}}, tilde{e}_i) 
+ tilde{R}
  (e^{-f}!tilde{e}_0, tilde{mathbf{S}}, tilde{mathbf{S}}, e^{-f}!tilde{e}_0) 
&quad= langle overline{nabla}_{!e_i} mathbf{S}, e_j rangle^2 
+ sum_{i=1}^n R(e_i, mathbf{S}, mathbf{S}, e_i) - 
smashoperator{sum_{alpha,beta=n+1}^{n+p}} S^{alpha}S^{beta} 
       overline{nabla}_{!alpha} overline{nabla}_{!beta} f 
+ e^{-4f} biggl( smashoperator[r]{sum_{alpha=n+1}^{n+p}} 
    S^{alpha} tilde{h}^{alpha}_{00} biggr)^2 
&qquad- smashoperator{sum_{alpha,beta=n+1}^{n+p}} 
S^{alpha}S^{beta} , 
overline{nabla}_{!alpha} f, overline{nabla}_{!beta}  f,.  
end{aligned}
end{equation}

end{document}