You can try this:
f[x_] = (((I!)^(Cos[x!] + Sin[I!]))!)^I - GoldenRatio^GoldenRatio!
sol = Solve[f[x] == 0, x]
f[x] /. sol // N
However, a complex number elevated to a complex number is a problematic concept:
ComplexPlot3D[Evaluate[N[f[x]]], {x, -10 - 10 I, 10 + 10 I},
PlotRange -> {-.1, 1.5}]
