Liver lesion detection and characterization presents a longstanding challenge for radiologists. Since liver lesions are mainly characterized from information obtained at both arterial and portal venous circulatory phases, current hepatic Computed tomography (CT) protocols involve intravenous contrast injection and subsequent multiple CT acquisitions. Because detection of lesions by CT often requires further investigation with MRI, improved differentiation CT capabilities are highly desirable. Recently developed imaging protocols for spectral photon-counting CT enable simultaneous mapping of arterial and portal-venous enhancements by injecting two different contrast agents sequentially, allowing robust pixel-to- pixel spatial alignment between the different contrast phases with a reduction of radiation exposure. Here we propose a method that allows to quantitatively and reliably distinguish between two contrast agents in a single dual-energy CT (DECT) acquisition by taking advantage of the unique abilities of modern self-learning algorithms for non-linear mapping, feature extraction, and feature representation. For this purpose, we designed a U-net architecture convolutional neural network (CNN). To overcome training data requirements, we utilizing clinical DECT images to simulate dual-contrast spectral datasets. With the unique network architecture and training datasets, we demonstrate reliable dual-contrast quantifications from DECT. Our results demonstrate an ability to quantify densities of water, iodine and gadolinium, with root mean square errors of 0.2 g/ml, 1.32 mg/ml and 1.04 mg/ml, respectively. While observing some material-cross artifacts, our model demonstrated a high robustness to noise. With the rapid increase in DECT usage, our results pave the way for improved diagnostics and better patient outcome with available hardware implementations.