A researcher testing the difference between two population means $\mu_1$ and $\mu_2$ uses a sample of $n_1 = 20$ and $n_2 = 25$. If the sample variances are $s_1^2 = 40$ and $s_2^2 = 60$, what is the standard error of the difference $\bar{x}_1 - \bar{x}_2$ assuming unequal variances?