Guice: inject dependency into @provides provider

I have a module in which I create a provider and that provider is needed as a dependency for another provider in the same module. However, this is not currently possible with my setup. How can I solve this issue? It should also be noted that all the dependencies are third party libraries and so I believe that I should not be binding this in my module (according to what Ive read).

Unfortunately, due to NDA I cannot provide the actual code, but an example of the dependency hierarchy can be seen below:

public MyModule extends AbstractModule {
    @Override
    protected void configure() {}

    @Singleton
    @Provides
    public Engine provideEngine(){
        Map<String, String> engineProperties = new HashMap<>();
        engineProperties.put("brand", "some brand");
        engineProperties.put("capacity", "2.6 litres");
        return new Engine(engineProperties);
    }

    @Inject
    @Provides
    public Car provideCar(Engine engine){
        Car car = new Car(engine);
        return car;
    }
}

Is short, I need to create a custom Engine, setting up some properties before hand and then use that Engine as a dependency for the Car creation (please note that i am fully aware that I cannot inject using the @Inject annotation in the module, however, I put this simply as a reference to what I want to achieve).