The ideal observer (IO) sets an upper performance limit among all observers and has been advocated for use in assessing and optimizing imaging systems. For joint detection-estimation tasks, the estimation ROC (EROC) curve has been proposed for evaluating the performance of observers. However, in practice, it is generally difficult to accurately approximate the IO that maximizes the area under the EROC curve (AEROC) for a general detection-estimation task. In this study, a hybrid method that employs machine learning is proposed to accomplish this. Specifically, a hybrid approach is developed that combines a multi-task convolutional neural network (CNN) and a Markov-Chain Monte Carlo (MCMC) method in order to approximate the IO for detectionestimation tasks. The multi-task CNN is designed to estimate the likelihood ratio and the parameter vector, while the MCMC method is employed to compute the utility-weighted posterior mean of the parameter vector. The IO test statistic is subsequently formed as the product of the likelihood ratio and the posterior mean of the parameter vector. Computer simulation studies were conducted to validate the proposed method, which include backgroundknown-exactly (BKE) and background-known-statistically (BKS) tasks. The proposed method provides a new approach for approximating the IO and may enable the application of EROC analysis for optimizing imaging systems.