Automated grading systems using deep convolution neural networks (DCNNs) have proven their capability and potential to distinguish between different breast cancer grades using digitized histopathological images. In digital breast pathology, it is vital to measure how confident a DCNN is in grading using a machine-confidence metric, especially with the presence of major computer vision challenging problems such as the high visual variability of the images. Such a quantitative metric can be employed not only to improve the robustness of automated systems, but also to assist medical professionals in identifying complex cases. In this paper, we propose Entropy-based Elastic Ensemble of DCNN models (3E-Net) for grading invasive breast carcinoma microscopy images which provides an initial stage of explainability (using an uncertainty-aware mechanism adopting entropy). Our proposed model has been designed in a way to (1) exclude images that are less sensitive and highly uncertain to our ensemble model and (2) dynamically grade the non-excluded images using the certain models in the ensemble architecture. We evaluated two variations of 3E-Net on an invasive breast carcinoma dataset and we achieved grading accuracy of 96.15% and 99.50%.