This paper investigates the precise structure of meromorphic solutions with hyper-order strictly less than 1 for non-linear difference equations of the form \( f^n(z)+q(z)e^{Q(z)}(\Delta _cf)^{m}=p_1e^{a_1z}+p_2e^{a_2z}, \) where m and n are positive integers, q(z) and Q(z) are nonzero polynomials with the additional condition that Q(z) is not a constant polynomial, and \(p_1, p_2, a_1, a_2\) are nonzero constants such that \(a_1\ne a_2\) . Our results show that when \(n\ge m+2\) , any meromorphic solution with hyper-order strictly less than 1 must be reduced to an exponential polynomial with \(\deg Q = 1\) . For \(n \ge m + 3\) , we derive exact forms of entire solutions, while for the critical cases \(n = m + 2\) (e.g., \(n = 3, 4\) ), we identify additional solution structures involving linear combinations of exponentials. Our theorems are supported by concrete examples, demonstrating their applicability.
