Noninvasively and accurately predicting the epidermal growth factor receptor (EGFR) mutation status is a clinically vital problem. Moreover, further identifying the most suspicious area related to the EGFR mutation status can guide the biopsy to avoid false negatives. Deep learning methods based on computed tomography (CT) images may improve the noninvasive prediction of EGFR mutation status and potentially help clinicians guide biopsies by visual methods. Inspired by the potential inherent links between EGFR mutation status and invasiveness information, we hypothesized that the predictive performance of a deep learning network can be improved through extra utilization of the invasiveness information. Here, we created a novel explainable transformer network for EGFR classification named gated multiple instance learning transformer (GMILT) by integrating multi-instance learning and discriminative weakly supervised feature learning. Pathological invasiveness information was first introduced into the multitask model as embeddings. GMILT was trained and validated on a total of 512 patients with adenocarcinoma and tested on three datasets (the internal test dataset, the external test dataset, and The Cancer Imaging Archive (TCIA) public dataset). The performance (area under the curve (AUC) = 0.772 on the internal test dataset) of GMILT exceeded that of previously published methods and radiomics-based methods (i.e., random forest and support vector machine) and attained a preferable generalization ability (AUC = 0.856 in the TCIA test dataset and AUC = 0.756 in the external dataset). A diameter-based subgroup analysis further verified the efficiency of our model (most of the AUCs exceeded 0.772) to noninvasively predict EGFR mutation status from computed tomography (CT) images. In addition, because our method also identified the "core area" of the most suspicious area related to the EGFR mutation status, it has the potential ability to guide biopsies.