E2E web test suites are prone to test dependencies due to the heterogeneous multi-tiered nature of modern web apps, which makes it difficult for developers to create isolated program states for each test case. In this paper, we present the first approach for detecting and validating test dependencies present in E2E web test suites. Our approach employs string analysis to extract an approximated set of dependencies from the test code. It then filters potential false dependencies through natural language processing of test names. Finally, it validates all dependencies, and uses a novel recovery algorithm to ensure no true dependencies are missed in the final test dependency graph. Our approach is implemented in a tool called TEDD and evaluated on the test suites of six open-source web apps. Our results show that TEDD can correctly detect and validate test dependencies up to 72% faster than the baseline with the original test ordering in which the graph contains all possible dependencies. The test dependency graphs produced by TEDD enable test execution parallelization, with a speed-up factor of up to 7x.