In this work, the investigation of Rossby-Khantadze waves with sheared zonal flows in E-ionosphere is presented. The spatially inhomogeneous Earth's angular velocity and background magnetic field are considered. The field inhomogeneity makes the coupling of Rossby and Khantadze waves. The numerical work of obtained linear frequencies is done. By using the method of multiple scale, we obtained a new Boussinesq nonlinear equation. Also, we obtain the travelling solitary structures.