async Task> GetE1Data()
{
    using(var MyCtx = new MyCtx())
    {
         return await MyCtx.E1.Where(bla bla bla).ToListAsync();
    }
}

async Task> GetE2Data()
{
    using(var MyCtx = new MyCtx())
    {
         return await MyCtx.E2.Where(bla bla bla).ToListAsync();
    }
}

async Task DoSomething()
{
    var t1 = GetE1Data();
    var t2 = GetE2Data();
    await Task.WhenAll(t1,t2);
    DoSomething(t1.Result, t2.Result);
}