You Do Need power plug adapter while traveling from Tonga to Solomon Islands.

Here is Why You Need An Adapter

The outlet and plug type used in Solomon Islands are G and I and in Tonga is I. This is how they look like.

Tonga

In Tonga, outlets of type I are in use.

Type I

Solomon Islands

In Solomon Islands, outlets of type G and I are in use.

Type G

Type I