Adding numbers ignoring text & negatives

I wish to add a column of numbers with 2 complications: 1. some cells contain negative numbers which I want to treat as positive numbers and 2. some cells may also contain text which I want to ignore, but still add the number in the cell (in which case text is always the same word - online). I have a formula to treat the negative numbers as positive ( =SUM(ABS(T3:T19)) ), but can't work out how to also include the numerical data in cells with text. In row '11' below I have shown the results I would like to generate.

Any help appreciated! Thx