BelT cipher uses a Pseudo-exponential substitution box. The $\lambda$ and z values selected for the the BelT gives a differential uniformity of 8. \begin{equation} exp_\lambda,_z (x) = \begin{cases} 0 & \text{if $\overline{x} =z$ }\\ \lambda^{x\boxplus+1} & \text{if $\overline{x} <z$ }\\ \lambda^x & \text{otherwise} \end{cases} \end{equation}
in Belt Sbox , the $\lambda= w^7+w^3+w$ where $w$ is is the generator of the multiplicative group of $F_2[]/(^8 + ^6 + ^5 + + 1)$, $z$ = 10, $\oplus$ is addition modulo 2 (xor).
The differential uniformity is computed using using $F(x) \oplus F(x\oplus a) = b$. I need help in finding number of b solutions in $exp_\lambda,_{10} (x) \oplus exp_\lambda,_{10} (x\oplus a)=b$