We propose a simple generalization of the matrix resolvent to a resolvent for real symmetric tensors T ∈ ⊗ p R N of order p ≥ 3. The tensor resolvent yields an integral representation for a class of tensor invariants and its singular locus can be understood in terms of the real eigenvalues of tensors.We then consider a random Gaussian (real symmetric) tensor. We show that in the large N limit the expected resolvent has a finite cut in the complex plane and that the associated "spectral density", that is the discontinuity at the cut, obeys a universal law which generalizes the Wigner semicircle law to arbitrary order.Finally, we consider a spiked tensor for p ≥ 3, that is the sum of a fixed tensor b v ⊗p with v ∈ R N (the signal) and a random Gaussian tensor T (the noise). We show that in the large N limit the expected resolvent undergoes a sharp transition at some threshold value of the signal to noise ratio b which we compute analytically.