Sony just announced the Xperia E4. It has a bigger screen than the Xperia E3, a similar a quad-core processor and 1GB RAM, plus a 5MP/1080p camera. It doesn’t have LTE though, what it does have is a dual-SIM version similar to the Xperia E3 and E1.
While it's not perfectly clear which phone is being replaced by the Xperia E4, but it will be Sony's first phone to launch with Android 5.0 Lollipop.
Update: in the promo video the OS version is listed as 4.4.4 KitKat. Hopefully Sony will get its story straight soon, but the earlier Android release looks more likely.
The phone is powered by an unknown chipset with a quad-core processor at 1.3GHz with 1GB of RAM. Update: apparently it's a MediaTek MT6582 chipset with four Cortex-A7 cores and a Mali-400MP2 GPU. The official specs page still says Adreno 330, which is clearly wrong.
The main camera is a 5MP shooter with 1080p video, while the selfie camera is a 2MP/720p unit. The selfie camera is an improvement over the VGA snapper of the Xperia E3 and you get double the storage out of the box – 8GB. There's a microSD card slot, of course.
For connectivity there's optional dual-SIM, 3G HSPA, Wi-Fi and Bluetooth 4.1. There's FM radio and Sony's usual assortment of audio-enhancing tech.
Since the Sony Xperia E4 and E4 Dual were announced without much noise we still don't know details like price and the launch time frame.
Note that these two are the E2003 and E2033, not the E2105/E2115 that leaked yesterday as the "Xperia E4."