During issue resolution, software developers rely on issue reports to discuss solutions for defects, feature requests, and other changes. These discussions contain proposed solutions--from design changes to code implementations--as well as their evaluations. Locating solution-related content is essential for investigating reopened issues, addressing regressions, reusing solutions, and understanding code change rationale. Manually understanding long discussions to identify such content can be difficult and time-consuming. This paper automates solution identification using language models as supervised classifiers. We investigate three applications--embeddings, prompting, and fine-tuning--across three classifier types: traditional ML models (MLMs), pre-trained language models (PLMs), and large language models (LLMs). Using 356 Mozilla Firefox issues, we created a dataset to train and evaluate six MLMs, four PLMs, and two LLMs across 68 configurations. Results show that MLMs with LLM embeddings outperform TF-IDF features, prompting underperforms, and fine-tuned LLMs achieve the highest performance, with LLAMAft reaching 0.716 F1 score. Ensembles of the best models further improve results (0.737 F1). Misclassifications often arise from misleading clues or missing context, highlighting the need for context-aware classifiers. Models trained on Mozilla transfer to other projects, with a small amount of project-specific data, further enhancing results. This work supports software maintenance, issue understanding, and solution reuse.