Speech signals in real-world environments are frequently affected by various distortions such as additive noise, reverberation, and bandwidth limitation, which may appear individually or in combination. Traditional speech enhancement methods typically rely on either masking, which focuses on suppressing non-speech components while preserving observable structure, or mapping, which seeks to recover clean speech through direct transformation of the input. Each approach offers strengths in specific scenarios but may be less effective outside its target conditions. We propose the Erase and Draw Network (EDNet), a versatile speech enhancement framework designed to handle a broad range of distortion types without prior assumptions about task or input characteristics. EDNet consists of two main components: (1) the Gating Mamba (GM) module, which adaptively combines masking and mapping through a learnable gating mechanism that selects between suppression (Erase) and reconstruction (Draw) based on local signal features, and (2) Phase Shift-Invariant Training (PSIT), a shift tolerant supervision strategy that improves phase estimation by enabling dynamic alignment during training while remaining compatible with standard loss functions. Experimental results on denoising, dereverberation, bandwidth extension, and multi distortion enhancement tasks show that EDNet consistently achieves strong performance across conditions, demonstrating its architectural flexibility and adaptability to diverse task settings.