Large language models (LLMs) are increasingly deployed not only to make decisions but to explain them. While AI decision fairness has been studied extensively, the fairness of AI explanations (whether LLMs justify decisions with equal quality, depth, tone, and linguistic sophistication across demographic groups) has received little attention. This paper introduces the Explanation Fairness Taxonomy (EFT), a framework comprising five formally defined, operationalizable dimensions: Verbosity Disparity, Sentiment Disparity, Epistemic Hedging Disparity, Decision-Linked Explanation Disparity, and Lexical Complexity Disparity. The taxonomy is instantiated in a controlled empirical study across 80 prompt templates, four consequential decision domains (hiring, medical triage, credit assessment, legal judgment), and five LLMs: GPT-4.1, Claude Sonnet, LLaMA 3.3 70B, GPT-OSS 120B, and Qwen3 32B. Two novel black-box metrics are introduced: the Hedging Density Score (HDS) and the Explanation Faithfulness Proxy (EFP), a heuristic indicator of decision-linked explanation variation. Across up to 400 prompt pairs, all eight EFT metrics show statistically significant disparities (Cohen's d ranging from small to large, all p_BH < 10^(-62)). Model choice is strongly associated with disparity magnitude: Qwen3 32B exhibits verbosity disparities 5.9x larger than LLaMA 3.3 70B. Two prompting-based mitigations show significant reductions in EFP disparity (78-95%) but no significant effect on stylistic dimensions, consistent with the hypothesis that stylistic explanation inequalities are encoded in pre-training distributions and are not resolvable through deployment-level instruction alone. A reproducible measurement framework is offered for explanation-level fairness auditing, with implications for AI regulation and deployment practice.