An object has 90.38 Joules of energy and it is traveling at 11.26 m/s. What is the objects mass?

I will have to assume that all of the energy number is kinetic energy, not potential, electrical, internal or any other type. The question should have clarified that. In that case,

(1/2) M V^2 = 90.38 (Joules)

Therefore,

M = 2*90.38/(11.26)^2 (kg)