Positional opening for Black
If I were you I would stick with the English opening as White.
As for Black, let us start with reply to
1.d4. I would strongly encourage you to learn Queen's gambit declined, as it is immune to transpositional tricks. The resulting positions require both theoretical knowledge and knowledge of typical plans. Your other option is Nimzo-Indian defense, but White can rule it out with a clever move order. Still, you can steer the game back into Queen's Gambit declined, with resulting lines being beneficial for Black, or you can learn Queen's-Indian defense. Also, when playing White, after
1.c4 e6 2.e4 is toothless, but
2.d4 d5 transposes into Queen's gambit declined/Nimzo-Indian/Queen's Indian, so this would save you a lot of learning time by reducing the amount of material you need to cover.
As for reply to
1.e4 there is French defense, Caro-Kann, or Petroff defense ( but be prepared to learn a lot about King's gambit ). Again, when playing White, after
1.c4 c6 2.e4! you sidestep many popular openings like Grunfeld, Slav/Semi-Slav and so on, and you transpose into Caro-Kann so I would suggest getting a book on it. The beauty of this move order is that you can transpose into Panov-Botvinnik attack, which is positional and requires knowledge from Black, else he may end up in a lost game, while you may play more or less on general principles. Either way, Black must invest more work here, as this line is critical for both sides. French defense may work too, as it is very solid, but you will still need to handle
1.c4 c6 and if you do not want to transpose into Caro-Kann be prepared to play against Slav or Semi-Slav.
I wonder if there are other solid openings which I could use as Black. Preferably, an opening for which there is a good book which explains the ideas and themes of the opening. Do you have any suggestions?
For French defense I find the book Nikita Vitiugov-The Complete French A Complete Black Repertoire quite useful.
For general ideas in Caro-Kann you can use Joe Gallagher-Starting Out The Caro-Kann and Petter Wells-Grandmaster Secrets The Caro-Kann and Karpov & Podgaets-Caro-Kann defense Panov Attack for Panov-Botvinnik Attack. For opening moves you have the Lars Schandorff-Grandmaster Repertoire 7 The Caro-Kann. These are more than enough to get you going.
For Nimzo-Indian and Queen's Indian defense you will have to find books yourself, since I do not play those defenses, and since there are so many books on those I do not wish to recommend bad ones.
As for Queen's Gambit Declined, you can start with Mathew Sadler-Queen's Gambit Declined since it covers typical plans for both sides very well. As for opening moves there are many books, seek on Amazon and you will find them. Unfortunately you will need most of them, in order to have your repertoire complete, and still it might not be enough. Take care especially for Alatortsev variation as it is very useful for Black if played right. Unfortunately I haven't found a good coverage on this line, and I must warn you that some novelties have been introduced from a year or two ago. I was lucky to find them, but God knows how many novelties I have missed.
That is it from me for now, if you have further questions leave a comment.