Explainable artificial intelligence (XAI) twin systems will be a fundamental enabler of zero-touch network and service management (ZSM) for sixth-generation (6G) wireless networks. A reliable XAI twin system for ZSM requires two composites: an extreme analytical ability for discretizing the physical behavior of the Internet of Everything (IoE) and rigorous methods for characterizing the reasoning of such behavior. In this paper, a novel neuro-symbolic explainable artificial intelligence twin framework is proposed to enable trustworthy ZSM for a wireless IoE. The physical space of the XAI twin executes a neural-network-driven multivariate regression to capture the time-dependent wireless IoE environment while determining unconscious decisions of IoE service aggregation. Subsequently, the virtual space of the XAI twin constructs a directed acyclic graph (DAG)-based Bayesian network that can infer a symbolic reasoning score over unconscious decisions through a first-order probabilistic language model. Furthermore, a Bayesian multi-arm bandits-based learning problem is proposed for reducing the gap between the expected explained score and the current obtained score of the proposed neuro-symbolic XAI twin. To address the challenges of extensible, modular, and stateless management functions in ZSM, the proposed neuro-symbolic XAI twin framework consists of two learning systems: 1) an implicit learner that acts as an unconscious learner in physical space, and 2) an explicit leaner that can exploit symbolic reasoning based on implicit learner decisions and prior evidence. Experimental results show that the proposed neuro-symbolic XAI twin can achieve around 96.26% accuracy while guaranteeing from 18% to 44% more trust score in terms of reasoning and closed-loop automation.