The development of machine learning applications has increased significantly in recent years, motivated by the remarkable ability of learning-powered systems to discover and generalize intricate patterns hidden in massive datasets. Modern learning models, while powerful, often exhibit a level of complexity that renders them opaque black boxes, resulting in a notable lack of transparency that hinders our ability to decipher their decision-making processes. Opacity challenges the interpretability and practical application of machine learning, especially in critical domains where understanding the underlying reasons is essential for informed decision-making. Explainable Artificial Intelligence (XAI) rises to meet that challenge, unraveling the complexity of black boxes by providing elucidating explanations. Among the various XAI approaches, feature attribution/importance XAI stands out for its capacity to delineate the significance of input features in the prediction process. However, most existing attribution methods have limitations, such as instability, when divergent explanations may result from similar or even the same instance. In this work, we introduce T-Explainer, a novel local additive attribution explainer based on Taylor expansion endowed with desirable properties, such as local accuracy and consistency, while stable over multiple runs. We demonstrate T-Explainer's effectiveness through benchmark experiments with well-known attribution methods. In addition, T-Explainer is developed as a comprehensive XAI framework comprising quantitative metrics to assess and visualize attribution explanations.