You will need to make some custom sprite materials.
Start out by making copies of Translucent Unlit sprite material. Select it in the content browser and hit Ctrl+w to duplicate.
Always make a copy in case you’re not happy with your changes, you won’t mess up the default material.
Additive and modulate support transparency. You just have to hook up the alpha channel from the sprite texture to the Opacity input like this:
Epic has a lot of those photoshop blend modes as material functions available from the get go.