Voltage regulation in alternator
There is a sign error in your calculation.
For unloaded operation, you have : V = E. So:
$$E_{nl} = 2000V$$

You want to calculate the variation of E you need to have in order to ensure that V stay constant when the alternator is loaded :

$$ E_l = V + R \times I + j \times X \times I $$
$$ E_l = 2000 + (0.8 + j \times 4) \times I = 1824 +  368j $$
$$ \left | E_l \right | = 1861 V $$

Note that El is lower than Enl because of the leading power factor.
Finally :
$$ {{1861 - 2000} \over {2000}} = -6.96\% $$