Do you mean something like this?
n = 4; eqs = DeleteCases[Flatten[Table[ If[i =!= j, \[Eta]^2 (t[i]^2 - w^2) == Product[(t[i] - t[j] - \[Eta])/(t[i] - t[j] + \[Eta]), {j, 1, n}]], {i, 1, n}, {j, i , n}]], Null]
Exactly! Thank you so much!
