Quantitative T2 and diffusion imaging provide important information about tissue microstructure. However, a joint knowledge of quantitative T2 and diffusion-derived measures can provide richer information about the microstructure that is not accessible when using these modalities independently. The standard approach for estimating the joint distributions of the T2-diffusion relies on the inverse Laplace transform. This transform is known to be unstable and difficult to invert. In this work, we introduce an alternative approach based on cumulant expansion, and extend the recently proposed multidimensional diffusion MRI framework ``Q-space Trajectory Imaging" (QTI) to include T2-relaxation modeling. The cumulants of the expansion include estimates of mean diffusion and T2 relaxation, as well as their variance and covariance. We demonstrate the feasibility of this approach in a healthy human brain.