The equation of state of QCD matter for temperatures near and above the quark-hadron transition (∼165 MeV) is inferred within a Bayesian framework through the comparison of data from the Relativistic Heavy Ion Collider and from the Large Hadron Collider to theoretical models. State-of-the-art statistical techniques are applied to simultaneously analyze multiple classes of observables while varying 14 independent model parameters. The resulting posterior distribution over possible equations of state is consistent with results from lattice gauge theory.