On the Non-Homogeneous Equation of the Eighth Degree withSix Unknowns x5-y5+(x3-y3)xy = p(z2-w2)2T3 .

We obtain infinitely many non-zero integer sextuples( , , , , , ) x y z w p T satisfying the non-homogeneous equation of degree eight with six unknowns given by 5 5 3 3 2 2 2 3 x y x y xy p z w T + = ( ) ( ) . Various interesting relations between the solutions and special numbers, namely, polygonal numbers, Pyramidal numbers, Star numbers, Stella Octangular numbers, Octahedral numbers, Pronic number, Jacobsthal number, JacobsthalLucas number, keynea number, Centered pyramidal numbers are exhibited.