The cornerstone of stroke care is expedient management that varies depending on the time since stroke onset. Consequently, clinical decision making is centered on accurate knowledge of timing and often requires a radiologist to interpret Computed Tomography (CT) of the brain to confirm the occurrence and age of an event. These tasks are particularly challenging due to the subtle expression of acute ischemic lesions and the dynamic nature of their appearance. Automation efforts have not yet applied deep learning to estimate lesion age and treated these two tasks independently, so, have overlooked their inherent complementary relationship. To leverage this, we propose a novel end-to-end multi-task transformer-based network optimized for concurrent segmentation and age estimation of cerebral ischemic lesions. By utilizing gated positional self-attention and CT-specific data augmentation, the proposed method can capture long-range spatial dependencies while maintaining its ability to be trained from scratch under low-data regimes commonly found in medical imaging. Furthermore, to better combine multiple predictions, we incorporate uncertainty by utilizing quantile loss to facilitate estimating a probability density function of lesion age. The effectiveness of our model is then extensively evaluated on a clinical dataset consisting of 776 CT images from two medical centers. Experimental results demonstrate that our method obtains promising performance, with an area under the curve (AUC) of 0.933 for classifying lesion ages ≤4.5 hours compared to 0.858 using a conventional approach, and outperforms task-specific state-of-the-art algorithms.