You may download shapefiles contininig roads data from OpenStreetMap from Geofabrik. Unzip the file and find the roads dataset.
Finding the roads data for a region in the world is in general not easy. In my own country, Norway, this is currently not possible since the National Mapping authority does not support roads data with proper temporal metadata. It would be very nice if such metadata was part of the Tanzanian data set. But I seriously doubt it.
Thank you for the advise, I am looking for main roads and thus do not need detailed road data. Further, I would like to see changes in roads over time. I am not sure if OpenStreetMap keeps historical maps.