In this paper, we consider the entire solutions of nonlinear difference equation f~3+ q(z)Δf = p_1e~(α_1z) +p_2e~(α_2z), where q is a polynomial, and p_1,p_2,α_1, and α_2 are nonzero constants with α_1≠α_2. It is showed that if f is a nonconstant entire solution of p_2(f) 1 to the above equation, then f(z) = e_1e~((α_1z)/3) + e_2e_1e~((α_2z)/3) , where e_1 and e_2 are two constants. Meanwhile, we give an affirmative answer to the conjecture posed by Zhang et al in [18].
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