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Multi-exposure image fusion (MEF) synthesizes multiple, differently exposed images of the same scene into a single, well-exposed composite. Retinex theory, which separates image illumination from scene reflectance, provides a natural framework to ensure consistent scene representation and effective information fusion across varied exposure levels. However, the conventional pixel-wise multiplication of illumination and reflectance inadequately models the glare effect induced by overexposure. To address this limitation, we introduce an unsupervised and controllable method termed Retinex-MEF. Specifically, our method decomposes multi-exposure images into separate illumination components with a shared reflectance component, and effectively models the glare induced by overexposure. The shared reflectance is learned via a bidirectional loss, which enables our approach to effectively mitigate the glare effect. Furthermore, we introduce a controllable exposure fusion criterion, enabling global exposure adjustments while preserving contrast, thus overcoming the constraints of a fixed exposure level. Extensive experiments on diverse datasets, including underexposure-overexposure fusion, exposure controlled fusion, and homogeneous extreme exposure fusion, demonstrate the effective decomposition and flexible fusion capability of our model. The code is available at https://github.com/HaowenBai/Retinex-MEF