Complementary label learning (CLL) is a weakly supervised learning paradigm that constructs a multi-class classifier only with complementary labels, specifying classes that the instance does not belong to. We reformulate CLL as an inverse problem that infers the full label information from the output space information. To be specific, we propose to split the inverse problem into two subtasks: positive label guessing (PLG) and negative label enhancement (NLE), collectively called PLNL. Specifically, we use well-designed criteria for evaluating the confidence of the model output, accordingly divide the training instances into three categories: highly-confident, moderately-confident and under-confident. For highly-confident instances, we perform PLG to assign them pseudo labels for supervised training. For moderately-confident and under-confident instances, we perform NLE by enhancing their complementary label set at different levels and train them with the augmented complementary labels iteratively. In addition, we unify PLG and NLE into a consistent framework, in which we can view all the pseudo-labeling-based methods from the perspective of negative label recovery. We prove that the error rates of both PLG and NLE are upper bounded, and based on that we can construct a classifier consistent with that learned by clean full labels. Extensive experiments demonstrate the superiority of PLNL over the state-of-the-art CLL methods, e.g., on STL-10, we increase the classification accuracy from 34.96\% to 55.25\%. The source code is available at https://github.com/yhli-ml/PLNL.