Suppose I have data $x$ and $y$, where $x$ is a count and $y$ is continuous. I would like to predict $x$ from $y$. 

Specifically, for my research question, $X$ can be viewed as being measured without error (it is fixed), whereas $Y$ is random.

Below is my data

    $x$:  [1] 1 2 3 4 5 6 7 8 9 10
  
    $y$:  [1] 1.0000 1.8002 2.4383 2.9353 3.3641 3.6847 3.9578 4.1610 4.3139 4.4667

What I am looking for is a regression technique that I can apply to the kind of data that I have supplied. 

Specifically, I would use the proposed regression method to answer a question such as "What is the value of $x$ for a corresponding $y$-value of $y$ = 5?" 

I am unaware of existing appropriate alternatives that could work in this setting. 

Any advice is greatly appreciated. 

  [1]: https://i.sstatic.net/v7NsI.png