Yes it is completely possible.
First, let us be clear. You aren't mainly talking about gaining muscle; Instead you are talking about looking better. Probably having a muscular and defined look. It's important to distinguish that because often the biggest obstacle in achieving the look you want is bodyfat, not muscle mass.
To illustrate the point:
A powerlifter at ~320lbs
The same powerlifter at ~260lbs
Where does he look more muscular and 'bigger'? Clearly in the latter picture.
Another example is Frank Zane who competed at around 185lbs:
So its clear: in order to achieve a 'muscular' look, bodyfat is actually more important than muscle mass. I say this to shift the discussion from that muscle mass is either as important or more than bodyfat. Because with that assertion a 'bulking' diet is more superior because its the fastest way to gain muscle.
Now back to your question.. is it possible to gain muscle and lose fat at the same time?
From my experience -and excuse the small bit of self promotion- yes. Is it as fast as if you tried to do one or the other? No.
Having said that, different circumstances require different approach:
Anyone above 20-25% bodyfat, and is concerned with how they look, should focus first on cutting bodyfat until they hit the low teens. That means a deficit diet.
Anyone who is sigifnantly underweight should focus on bulking/gaining until hitting a good weight. That means a gaining diet.
Anyone who has a bodyfat in the mid/low teens, have low/moderate muscle mass should do a composition shift or gain muscle/lose fat diet.
As for you, the best way to solve your problems is by addressing your diet, since nutrition is #1 when it comes to reducing bodyfat. Considering you have visible love handles you should aim to do a cutting diet where you eat at a caloric deficit until you reach the desired bodyfat level. You won't gain a lot of muscle if any during that phase, but that will get you looking the best possible in the shortest amount of time. From there you can transition to a composition shift diet where you either eat at maintenance or at a slight deficit or surplus depending if you want to focus more on the fat loss or muscle gain side.
Advanced bodybuilder's methods do not apply or translate to intermedia lifter since bodybuilders are working with an already large amount of muscle mass, not to mention the large amount of exogenous hormones and drugs that they take -it is impossible for Fabiola to look the way she does without exogenous testosterone for example.
Also bodybuilders are focused on how they 'peak'. So a gaining and cutting cycle makes perfect sense. But the average person isn't going to sacrifice 6 months of the year looking bloated and fat in order to look good for 3 weeks.
Here's one of my latest clients demonstrating how being leaner makes you look so much bigger even if you are 40lbs lighter overall.