For both of the tests my daughter took, there was no difference between her English score and the combined English/Writing score (included at the bottom of the score report). Do some people's scores change when you lump the two together? Otherwise, I don't see what the point is.
The combined English/Writing score was included on ACT score reports from the introduction of the Writing test up through the June 2015 ACT testing date. The combined score wasn't included in the composite (which was still the average of your English, Math, Reading, and Science scores), but this score allowed schools easier comparison between SAT and ACT scores, since SAT Writing includes both grammar content (like ACT English) and a mandatory essay (like the ACT Writing test).
Since September 2015, however, ACT score reports have instead begun to include a combined English/Reading/Writing score, so any tests taken since then will not include the old English/Writing subscore. Instead, your score report will have a simple average of your English, Reading, and Writing scores. Just like before, though, your combined score won't be used to calculate your composite score - just your English, Math, Reading, and Science scores, as always.