Hermitian solution and positive semidefinite solution to tensor equation can be regarded as an extension of the matrix equation. According to the structure of the solution, a special solution to the tensor equation is found, and the general solution to the homogeneous equation is established corresponding to the tensor equation. The necessary and sufficient conditions for the existence and the explicit expressions for these two solutions to the tensor equation are presented.The necessary and sufficient conditions for the existence of Hermitian solution and positive semi-definite solution of tensor equations show that the properties of Hermitian and positive semi-definite solutions of matrix equation and the explicit expressions of general solutions can be extended to tensor equations.