Electrical impedance tomography (EIT) is a noninvasive and non-radiative medical imaging technique based on detecting the inhomogeneous electrical properties of the tissue. The inverse problem of EIT is a highly nonlinear ill-posed problem, which is the main reason that affects image quality. Our goal is to solve the EIT inverse problem using the nonlinear mapping properties of artificial neural networks (ANNs) and convolutional neural networks (CNNs). In this paper, the adaptive moment estimation (ADAM) optimization method and mean-square-error (MSE) function are used to train an ANN to solve the inverse problem and a CNN to process the ANN image. The networks are trained on datasets of simulated data, and tested on datasets of simulated data and experimental data. Results for time-difference EIT (td-EIT) images are presented using simulated EIT data from EIDORS and experimental EIT data from our EIT systems. The results are used to compare the proposed method with the one-step Gauss-Newton linear method and RBFNN method. The proposed method offers improved resolution (RES), low position error (PE) and excellent artefact removal compared to the existing methods. The experimental results show that our method can improve the RES by 50 to 70 percent and reduce the PE by 60 to 70 percent. The improvements in RES and processing speed are essential for clinical EIT measurement of dynamic physiological processes.