This paper introduces a novel incremental distributed back-end algorithm for Collaborative Simultaneous Localization and Mapping (C-SLAM). For real-world deployments, robotic teams require algorithms to compute a consistent state estimate accurately, within online runtime constraints, and with potentially limited communication. Existing centralized, decentralized, and distributed approaches to solving C-SLAM problems struggle to achieve all of these goals. To address this capability gap, we present Incremental Manifold Edge-based Separable ADMM (iMESA) a fully distributed C-SLAM back-end algorithm that can provide a multi-robot team with accurate state estimates in real-time with only sparse pair-wise communication between robots. Extensive evaluation on real and synthetic data demonstrates that iMESA is able to outperform comparable state-of-the-art C-SLAM back-ends.