First, we need to work out the number of squares in each row.
Each tetromino takes up 4 squares, and each contributes twice to the total squares in rows and columns.
So each tetromino contributes 8 squares.
There are 10 * 8 = 80 squares and 16 rows/columns, so there are 80 / 16 = 5 squares per row/column.
Then, some trial-and-error does the trick:
I started with this configuration, which looked promising:
Then messed around until I found an inner configuration that worked.
An alternative, asymmetric solution: