This paper proposes a framework of explaining anomalous machine sounds in the context of anomalous sound detection~(ASD). While ASD has been extensively explored, identifying how anomalous sounds differ from normal sounds is also beneficial for machine condition monitoring. However, existing sound difference captioning methods require anomalous sounds for training, which is impractical in typical machine condition monitoring settings where such sounds are unavailable. To solve this issue, we propose a new strategy for explaining anomalous differences that does not require anomalous sounds for training. Specifically, we introduce a framework that explains differences in predefined timbre attributes instead of using free-form text captions. Objective metrics of timbre attributes can be computed using timbral models developed through psycho-acoustical research, enabling the estimation of how and what timbre attributes have changed from normal sounds without training machine learning models. Additionally, to accurately determine timbre differences regardless of variations in normal training data, we developed a method that jointly conducts anomalous sound detection and timbre difference estimation based on a k-nearest neighbors method in an audio embedding space. Evaluation using the MIMII DG dataset demonstrated the effectiveness of the proposed method.