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Plot[{Abs[3 - t^2] + Abs[t - 1] - t^2, 2*Sin[t]}, {t, -8, 8}] 

Experimenting with the initial guess,

FindRoot[{Abs[3 - t^2] + Abs[t - 1] - t^2 == 2*Sin[t]}, {t, #}] & /@ {0, 6} 

{{t -> 0.885124}, {t -> 3.43039}}